Chapter 5

Factor each expression. $$ 5 t^{2}+28 t+32 $$

Physics The equation for the motion of a projectile fired straight up at an minitial velocity of \(64 \mathrm{ft} / \mathrm{s} h=64 t-16 t^{2}\) , where \(h\) is the height in feet and \(t\) is the time in seconds. Find the time the projectile needs to reach its highest point. How high it will go?

Solve each equation using the Quadratic Formula. Find the exact solutions. Then approximate any radical solutions. Round to the nearest hundredth. $$ 2 x^{2}+x=\frac{1}{2} $$

Rewrite each equation in vertex form. $$ y=-2 x^{2}+6 x+1 $$

Simplify each expression. $$ (-3-5 i)+(4-2 i) $$

Solve each equation by graphing. Give each answer to at most two decimal places. $$ x^{2}+4 x=6 $$

Factor each expression. $$ 2 x^{2}-27 x+36 $$

Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary. $$ x^{2}+4 x+5=0 $$

Rewrite each equation in vertex form. $$ y=x^{2}+4 x+1 $$

Simplify each expression. $$ (7+9 i)+(-5 i) $$

Solve each equation by graphing. Give each answer to at most two decimal places. $$ 2 x^{2}-2 x-5=0 $$

Factor each expression. $$ 3 x^{2}+7 x-20 $$

Sketch each parabola using the given information. vertex \((3,6), y\) -intercept 2

Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary. $$ x^{2}-4 x-5=0 $$

Rewrite each equation in vertex form. $$ y=2 x^{2}-8 x+1 $$

Simplify each expression. $$ 6-(8+3 i) $$

Factor each expression. $$ 5 y^{2}+12 y-32 $$

The graph of each function contains the given point. Find the value of \(c .\) $$ y=x^{2}+c ;(0,3) $$

Sketch each parabola using the given information. vertex \((-1,-4), y\) -intercept 3

Rewrite each equation in vertex form. $$ y=-x^{2}-2 x+3 $$

Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary. $$ 4 x^{2}+20 x+25=0 $$

Simplify each expression. $$ (12+5 i)-(2-i) $$

Multiple Choice The period of a pendulum is the time the pendulum takes to swing back and forth. The function \(\ell=0.81 t^{2}\) relates the length \(\ell\) in feet of a pendulum to the time \(t\) in seconds that it takes to swing back and forth. The convention center in Portland, Oregon, has the longest pendulum in the United States. The pendulum's length is 90 ft. Find the period. A 8.5 seconds B 10.5 seconds C 90 seconds D 111 seconds

Factor each expression. $$ 7 x^{2}-8 x-12 $$

Write each function in vertex form. $$ y=2 x^{2}-5 x+12 $$

The graph of each function contains the given point. Find the value of \(c .\) $$ y=x^{2}-c ;(4,8) $$

Sketch each parabola using the given information. vertex \((0,5),\) point \((1,-2)\)

Rewrite each equation in vertex form. Then find the vertex of the graph. $$ y=-4 x^{2}-5 x+3 $$

Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary. $$ 2 x^{2}+x+28=0 $$

Simplify each expression. $$ (-6-7 i)-(1+3 i) $$

Open-Ended Write an equation in standard form that you can solve by factoring and an equation that you cannot solve by factoring.

Factor each expression. $$ 2 z^{2}+z-28 $$

Write each function in vertex form. $$ y=-2 x^{2}+8 x+3 $$

Sketch each parabola using the given information. vertex \((2,3),\) point \((6,9)\)

The graph of each function contains the given point. Find the value of \(c .\) $$ y=-5 x^{2}+c ;(2,-14) $$

Rewrite each equation in vertex form. Then find the vertex of the graph. $$ y=\frac{1}{2} x^{2}-5 x+12 $$

Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary. $$ 2 x^{2}+7 x-15=0 $$

Simplify each expression. $$ (-2 i)(5 i) $$

Factor each expression. $$ 3 x^{2}+8 x-16 $$

Write each function in vertex form. $$ y=\frac{9}{4} x^{2}+3 x-1 $$

The graph of each function contains the given point. Find the value of \(c .\) $$ y=2 x^{2}+c ;\left(-\frac{3}{4},-\frac{1}{4}\right) $$

Rewrite each equation in vertex form. Then find the vertex of the graph. $$ y=-\frac{1}{5} x^{2}+\frac{4}{5} x+\frac{11}{5} $$

Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary. $$ 6 x^{2}-2 x+5=0 $$

Simplify each expression. $$ (4-3 i)(5+2 i) $$

Solve each equation by factoring, by taking square roots, or by graphing. If necessary, round your answer to the nearest hundredth. $$ x^{2}+6 x+5=45 $$

Factor each expression. $$ 28 k^{2}+13 k-6 $$

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

The graph of each function contains the given point. Find the value of \(c .\) $$ y=-\frac{3}{4} x^{2}+c ;\left(3,-\frac{1}{2}\right) $$

Manufacturing An electronics company has a new line of portable radios with CD players. Their research suggests that the daily sales \(s\) for the new product can be modeled by \(s=-p^{2}+120 p+1400,\) where \(p\) is the price of each unit. a. Find the vertex of the graph of the function by completing the square. b. Describe a reasonable domain and range for the sales function. Explain. c. What price gives maximum daily sales? What are the maximum daily sales?

Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary. $$ 2 x^{2}+7 x=-6 $$