Chapter 5

Simplify each expression. $$ (8+i)(2+7 i) $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ x^{2}-11 x+24=0 $$

Factor each expression. $$ x^{2}+2 x+1 $$

Sketch each parabola. Identify the axis of symmetry. $$ y=-3(x-2)^{2} $$

The graph of each function contains the given point. Find the value of \(c .\) $$ y=(x+c)^{2} ;(10,0) $$

Writing Explain the process of rewriting \(x^{2}+8 x+11=0\) as \((x+4)^{2}=5\)

Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary. $$ x^{2}-12 x+36=0 $$

Simplify each expression. $$ (-6-5 i)(1+3 i) $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ 3 x^{2}=27 $$

Factor each expression. $$ t^{2}-14 t+49 $$

Sketch each parabola. Identify the axis of symmetry. $$ y=5(x+0.3)^{2}-10 $$

Sports The height of a punted football can be modeled with the quadratic function \(h=-0.01 x^{2}+1.18 x+2 .\) The horizontal distance in feet from the point of impact with the kicker's foot is \(x,\) and \(h\) is the height of the ball in feet. a. Find the vertex of the graph of the function by completing the square. b. What is the maximum height of the punt? c. The nearest defensive player is 5 ft horizontally from the point of impact. How high must the player reach to block the punt? d. Suppose the ball was not blocked but continued on its path. How far down field would the ball go before it hit the ground? e. Critical Thinking The linear equation \(h=1.13 x+2\) could model the path of the football shown in the graph. Why is this not a good model?

Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary. $$ x^{2}=8 x-16 $$

Simplify each expression. $$ (-6 i)^{2} $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ 2 x^{2}-5 x-3=0 $$

Factor each expression. $$ x^{2}-18 x+81 $$

Sketch each parabola. Identify the axis of symmetry. $$ y=-0.5(x-2)^{2}-5 $$

Match each function with its graph. $$ y=-\frac{1}{2} x^{2}-2 x+1 $$

Find the value of \(k\) that would make the left side of each equation a perfect square trinomial. $$x^{2}+k x+25=0$$

Simplify each expression. $$ (9+4 i)^{2} $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ x^{2}+2 x=6-6 x $$

Factor each expression. $$ 4 n^{2}-20 n+25 $$

Begin with the parent \(y=x^{2}\) graph. Show how to transform it to graph each function below. Draw the final graph in a different color. $$ y=-2(x+1)^{2}+1 $$

Critical Thinking What is the minimum number of data points you need to find a quadratic model for a data set? Explain.

Find the value of \(k\) that would make the left side of each equation a perfect square trinomial. $$x^{2}-k x+100=0$$

Solve each equation using any method. When necessary, round real solutions to the nearest hundredth. For imaginary solutions, write exact solutions. $$ x^{2}=11 x-10 $$

Solve each equation. Check your answers. $$ x^{2}+25=0 $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ 6 x^{2}+13 x+6=0 $$

Factor each expression. $$ 9 x^{2}+48 x+64 $$

Begin with the parent \(y=x^{2}\) graph. Show how to transform it to graph each function below. Draw the final graph in a different color. $$ y=0.2(x-12)^{2}-3 $$

How are the graphs of \(y=x^{2}\) and \(y=|x|\) similar? How are they different?

Find the value of \(k\) that would make the left side of each equation a perfect square trinomial. $$ x^{2}-k x+121=0 $$

Solve each equation using any method. When necessary, round real solutions to the nearest hundredth. For imaginary solutions, write exact solutions. $$ 5 x^{2}=210 x $$

Solve each equation. Check your answers. $$ 2 x^{2}+1=0 $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ 2 x^{2}+8 x=5 x+20 $$

Factor each expression. $$ 81 z^{2}+36 z+4 $$

Business The Big Brick Bakery sells more bagels when it reduces its prices, but then its profit changes. The function \(y=-1000(x-0.55)^{2}+300\) models the bakery's daily profit in dollars, from selling bagels, where \(x\) is the price of a bagel in dollars. The bakery wants to maximize the profit. a. What is the domain of the function? Can \(x\) be negative? Explain. b. Find the daily profit for selling bagels for \(\$ .40\) each; for \(\$ .85\) each. c. What price should the bakery charge to maximize its profit from bagels? d. What is the maximum profit?

A parabola contains the points \((0,-4),(2,4),\) and \((4,4) .\) Find the vertex.

Find the value of \(k\) that would make the left side of each equation a perfect square trinomial. $$ x^{2}+k x+64=0 $$

Solve each equation using any method. When necessary, round real solutions to the nearest hundredth. For imaginary solutions, write exact solutions. $$ 4 x^{2}+4 x=3 $$

Solve each equation. Check your answers. $$ 3 s^{2}+2=-62 $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ 7 x^{2}-243=0 $$

Factor each expression. $$ x^{2}-4 $$

Write the equation of each parabola in vertex form. vertex \((1,2),\) point \((2,-5)\)

A model for the height of an arrow shot into the air is \(h(t)=-16 t^{2}+72 t+5\) where \(t\) is time and \(h\) is height. Without graphing, consider the function's graph. a. What can you learn by finding the graph's intercept with the \(h\) -axis? b. What can you learn by finding the graph's intercept(s) with the \(t\) -axis?

Find the value of \(k\) that would make the left side of each equation a perfect square trinomial. $$ x^{2}-k x+81=0 $$

Solve each equation using any method. When necessary, round real solutions to the nearest hundredth. For imaginary solutions, write exact solutions. $$ 2 x^{2}+4 x=10 $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ 3 x^{2}+7 x=9 $$

Write the equation of each parabola in vertex form. vertex \((3,6), y-\) intercept 2

Factor each expression. $$ c^{2}-64 $$