Quadratic Functions and Inequalities

A tour bus in the historic district of Savannah, Georgia, serves 300 customers a day. The charge is \(8 per person. The owner estimates that the company would lose 20 passengers a day for each \)1 fare increase. What charge would give the most income for the company?

A tour bus in the historic district of Savannah, Georgia, serves 300 customers a day. The charge is \(8 per person. The owner estimates that the company would lose 20 passengers a day for each \)1 fare increase. If the company raised their fare to this price, how much daily income should they expect to bring in?

WRITING IN MATH

A rectangle is inscribed in an isosceles triangle as shown. Find the dimensions of the inscribed rectangle with maximum area. (Hint: Use similar triangles.)

Write an expression for the minimum value of a function of the form $y=a{x}^2+c$, where $a>0$. Explain your reasoning. Then use this function to find the minimum value of $y=8.6x^2-12.5$

WRITING IN MATH Answer the question that was posed at the beginning of the lesson.

How can income from a rock concert be maximized?

Include the following in your answer:

• an explanation of why income increases and then declines as the ticket price

increases, and

• an explanation of how to algebraically and graphically determine what ticket

price should be charged to achieve maximum income.

The graph of which of the following equations is symmetrical about the y-axis?

1. $y=x^2+3x-1$
2. $y=-x^2+x$
3. $y=6x^2+9$
4. $y=3x^2-3x+1$

Which of the following tables represents a quadratic relationship between the two variables x and y?

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

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

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

$f\left(x\right)=-5x^2+8x$

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

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

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

$f\left(x\right)=-6x^2+9x$

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

$f\left(x\right)=7x^2+4x+1$

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

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

Simplify

$i^{14}$

Simplify

$\left(4-3i\right)-\left(5-6i\right)$

Simplify

$\left(7+2i\right)\left(1-i\right)$

Solve each equation

$5-\sqrt{b+2}=0$

Solve each equation

$\sqrt[3]{x+5}+6=4$

1. Define each term and explain how they are related.

a. solution      b. root          c. zero of a function        d. x-intercept

Give an example of a quadratic function and state its related quadratic equation. 

Explain how you can estimate the solutions of a quadratic equation by examining the graph of its related function.

Use the related graph of each equation to determine its solutions $x^2+3x-4=0$.

Use the related graph of each equation to determine its solutions.

$2x^2+2x-4=0$

Use the related graph of each equation to determine its solutions.

$x^2+8x+16=0$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$-x^2-7x=0$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$x^2-2x-24=0$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$x^2+3x=28$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$25+x^2+10x=0$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$4x^2-7x-15=0$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$2x^2-2x-3=0$

NUMBER THEORY Use a quadratic equation to find two real numbers whose sum is 5 and whose product is -14, or show that no such numbers exist.

Use the related graph of each equation to determine its solutions.

$x^2-6x=0$

Use the related graph of each equation to determine its solutions. $x^2-6x+9=0$

Use the related graph of each equation to determine its solutions.

$-2x^2-x+6=0$

Use the related graph of each equation to determine its solutions.

$-0.5x^2=0$

Use the related graph of each equation to determine its solutions.

$2x^2-5x-3=0$

Use the related graph of each equation to determine its solutions.

$-3x^2-1=0$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$x^2-3x=0$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$-x^2+4x=0$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$x^2+4x-4=0$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$x^2-2x-1=0$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$-x^2+x=-20$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$x^2-9x=-18$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$14x+x^2+49=0$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$-12x+x^2=-36$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$2x^2-3x=9$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$4x^2-8x=5$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$2x^2=-5x+12$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$2x^2=x+15$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$x^2+3x-2=0$