Chapter 9

Find and correct the error at the right. $$ \begin{array}{r} {x^{2}+36=0} \\ {x^{2} =-36} \\ {x=\pm 6} \end{array} $$

Graph the exponential function. (Lesson 8.3) $$ y=\left(\frac{1}{3}\right)^{x} $$

In Exercises \(49-51\), sketch the graphs of the three functions in the same coordinate plane. Then describe how the three parabolas are similar to each other and how they are different. $$ \begin{aligned} &y=x^{2}+x+1\\\ &y=x^{2}+2 x+1\\\ &y=x^{2}+3 x+1 \end{aligned} $$

Use a graphing calculator to approximate the solutions of the equation. $$\frac{5}{4} x^{2}+15 x+40=0$$

Write the quadratic equation in standard form. Then solve using the quadratic formula. $$x^{2}+3 x=-2$$

You can jump with an initial velocity of 12 feet per second. You need to jump 2.2 feet to dunk a basketball. Use the vertical motion model \(h=-16 t^{2}+v t+s\) to find if you can dunk the ball. Justify your answer.

Simplify the expression. $$ \sqrt{\frac{3}{5}} $$

Determine whether the number is a perfect square. $$ 10,000 $$

Use a calculator to solve the equation. Round the result to the nearest hundredth. $$ 4 x^{2}-3=57 $$

Graph the exponential function. (Lesson 8.3) $$ y=2\left(\frac{1}{4}\right)^{x} $$

In Exercises \(49-51\), sketch the graphs of the three functions in the same coordinate plane. Then describe how the three parabolas are similar to each other and how they are different. $$ \begin{array}{l} {y=x^{2}-x+1} \\ {y=x^{2}-x+3} \\ {y=x^{2}-x-2} \end{array} $$

Use the following information. Scientists use a state of free fall to simulate a gravity-free environment called microgravity. In microgravity conditions, the distance \(d\) (in meters) that an object that is dropped falls in \(t\) seconds can be modeled by the equation \(d=4.9 t^{2}\). In Japan a 490 -meter-deep mine shaft has been converted into a free-fall facility. This creates the longest period of free fall currently available on Earth. How long is a period of free fall in this facility? Solve the problem algebraically.

Write the quadratic equation in standard form. Then solve using the quadratic formula. $$5=x^{2}+6 x$$

For which value of \(c\) will \(-3 x^{2}+6 x+c=0\) not have a real solution? A) \(c<-3\) B) \(c=-3\) C) \(c>-3\) D) \(c=3\)

Simplify the expression. $$ \sqrt{\frac{5}{15}} $$

Determine whether the number is a perfect square. $$ \frac{9}{4} $$

Use a calculator to solve the equation. Round the result to the nearest hundredth. $$ 6 y^{2}+22=34 $$

Graph the exponential function. (Lesson 8.3) $$ y=\left(\frac{2}{3}\right)^{x} $$

Use the following information. Scientists use a state of free fall to simulate a gravity-free environment called microgravity. In microgravity conditions, the distance \(d\) (in meters) that an object that is dropped falls in \(t\) seconds can be modeled by the equation \(d=4.9 t^{2}\). In Japan a 490 -meter-deep mine shaft has been converted into a free-fall facility. This creates the longest period of free fall currently available on Earth. How long is a period of free fall in this facility? Use a graphing calculator to check your answer by graphing the related function \(y=4.9 x^{2}-490\).

Write the quadratic equation in standard form. Then solve using the quadratic formula. $$5 x+2=2 x^{2}$$

How many real solutions does \(x^{2}-10 x+25=0\) have? F) No solutions G) One solution H) Two solutions J) Many solutions

Simplify the expression. $$ \sqrt{\frac{3}{21}} $$

Determine whether the number is a perfect square. $$ \frac{1}{2} $$

Use a calculator to solve the equation. Round the result to the nearest hundredth. $$ 2 x^{2}-4=10 $$

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 4 \% $$

MULTIPLE CHOICE What are the coordinates of the vertex of the graph of \(y=-2 x^{2}+8 x-5 ?\) $$ \begin{aligned} &F.)\quad (-2,-29) &G.)\quad (2,3) &H.)\quad (2,7) &J.)\quad (4,-5) \end{aligned} $$

What are the \(x\) -intercepts of \(y=x^{2}-2 x-3 ?\) (A) 1 and \(-3\) (B) 2 and \(-3\) (C) 6 and \(-1\) (D) 3 and \(-1\)

Write the quadratic equation in standard form. Then solve using the quadratic formula. $$5 x-2 x^{2}+15=8$$

Solve the inequality. Then graph the solution. \(2 \leq x+1<5\)

Simplify the expression. $$ \sqrt{\frac{4}{10}} $$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$ \sqrt{5} $$

Use a calculator to solve the equation. Round the result to the nearest hundredth. $$ 3 x^{2}+7=31 $$

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 392 \% $$

MULTIPLE CHOICE What is the axis of symmetry of the graph of \(y=x^{2}+3 x-2 ?\) $$ \begin{aligned} &A.)\quad x=-\frac{17}{4} &B.)\quad x=-\frac{3}{2} &C.)\quad x=\frac{3}{2} &D.)\quad x=\frac{19}{4} \end{aligned} $$

Write the quadratic equation in standard form. Then solve using the quadratic formula. $$-2+x^{2}=-x$$

Solve the inequality. Then graph the solution. \(8>2 x>-4\)

Simplify the expression. $$ \sqrt{\frac{4}{3}} $$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$ \sqrt{25} $$

Use a calculator to solve the equation. Round the result to the nearest hundredth. $$ 7 n^{2}-6=15 $$

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 45 \% $$

Graph the system of linear inequalities. $$ \begin{aligned} &x-3 y \geq 3\\\ &x-3 y<12 \end{aligned} $$

At lunch, you order 1 pasta dish and 1 type of salad. Your friend orders 1 pasta dish and 2 types of salads. The restaurant charges the same price for each pasta dish and the same price for each salad. Your bill is \(\$ 7.90\) and your friend's bill is \(\$ 9.85 .\) How much did each pasta dish and each salad cost?

Write the quadratic equation in standard form. Then solve using the quadratic formula. $$x^{2}-2 x=3$$

Solve the inequality. Then graph the solution. \(-12<2 x-6<4\)

Simplify the expression. $$ \sqrt{\frac{1}{11}} $$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$ \sqrt{13} $$

Use a calculator to solve the equation. Round the result to the nearest hundredth. $$ 5 x^{2}-12=5 $$

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 500 \% $$

Graph the system of linear inequalities. $$ \begin{array}{r} {x+y \leq 5} \\ {x \geq 2} \\ {y \geq 0} \end{array} $$

Use the substitution method or linear combinations to solve the linear system and tell how many solutions the system has. $$\begin{array}{r} {-2 x+8 y=11} \\ {x+6 y=2} \end{array}$$