Quadratic Functions and Inequalities

Give an example of a quadratic function. Identify its quadratic term, linear term, and constant term.

Identify the vertex and the equation of the axis of symmetry for each function graphed below.

State whether the graph of each quadratic function opens up or down. Then state whether the function has a maximum or minimum value.

$\begin{array}{l}a.f\left(x\right)=3x^2+4x-5\\ b.f\left(x\right)=-2x^2+9\\ c.f\left(x\right)=-5x^2-8x+2\\ d.f\left(x\right)=6x^2-5x\end{array}$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.
4. $f\left(x\right)=-4x^2$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=x^2+2x$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=-x^2+4x-1$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=x^2+8x+3$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=2x^2-4x+1$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=3x^2+10x$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=-x^2+7$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=x^2-x-6$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=4x^2+12x+9$

Due to increased production costs, the Daily News must increase its subscription rate. According to a recent survey, the number of subscriptions will decrease by about 1250 for each 25¢ increase in the subscription rate. What weekly subscription rate will maximize the newspaper's income from subscriptions?

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=2x^2$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=-5x^2$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=x^2+4$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=x^2-9$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=2x^2-4$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=3x^2+1$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=x^2-4x+4$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=x^2-9x+9$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=x^2-4x-5$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=x^2+12x+36$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=3x^2+6x-1$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=-2x^2+8x-3$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=-3x^2-4x$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=2x^2+5x$

Complete parts a-c for each quadratic function.

        a. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.

           b. Make a table of values that includes the vertex.

          c. Use this information to graph the function.

$f\left(x\right)=0.5x^2-1$

Complete parts a-c for each quadratic function.

      a. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.

       b. Make a table of values that includes the vertex.

       c. Use this information to graph the function.

$f\left(x\right)=-0.25x^2-3x$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=\frac{1}{2}{x}^2+3x+\frac{9}{2}$

Complete parts a-c for each quadratic function.

1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
2. Make a table of values that includes the vertex.
3. Use this information to graph the function.

$f\left(x\right)=x^2-\frac{2}{3}x-\frac{8}{9}$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=3x^2$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=-x^2-9$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=x^2-8x+2$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=x^2+6x-2$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=4x-x^2+1$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=3-x^2-6x$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=2x+2x^2+5$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=x-2x^2-1$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=-7-3x^2+12x$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=-20x+5x^2+9$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=-\frac{1}{2}{x}^2-2x+3$

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

$f\left(x\right)=\frac{3}{4}{x}^2-5x-2$

The shape of each arch supporting the Exchange House can be modeled by $h\left(x\right)=-0.025x^2+2x$, where $h\left(x\right)$ represents the height of the arch and x represents the horizontal distance from one end of the base in meters.

Write the equation of the axis of symmetry, and find the coordinates of the vertex of the graph of $h\left(x\right)$.

The shape of each arch supporting the Exchange House can be modeled by $h\left(x\right)=-0.025x^2+2x$, where h(x) represents the height of the arch and x represents the horizontal distance from one end of the base in meters.

According to this model, what is the maximum height of the arch?

An object is fired straight up from the top of a 200-foot tower at a velocity of 80 feet per second. The height h(t) of the object t seconds after firing is given by $h\left(t\right)=-16t^2+80t+200$. Find the maximum height reached by the object and the time that the height is reached.

An object is fired straight up from the top of a 200-foot tower at a velocity of 80 feet per second. The height h(t) of the object t seconds after firing is given by $h\left(t\right)=-16t^2+80t+200$. Interpret the meaning of the y-intercept in the context of this problem.

Steve has 120 feet of fence to make a rectangular kennel for his dogs. He will use his house as one side. Write an algebraic expression for the kennel’s length.

Steve has 120 feet of fence to make a rectangular kennel for his dogs. He will use his house as one side. What dimensions produce a kennel with the greatest area?

Steve has 120 feet of fence to make a rectangular kennel for his dogs. He will use his house as one side. Find the maximum area of the kennel.