91Ó°ÊÓ

Concept Check Write a sentence describing the first step you would take to solve each equation. Do not actually solve. $$\left(x^{2}+x\right)^{2}-8\left(x^{2}+x\right)+12=0$$

The solution set of the inequality \(x^{2}+x-12<0\) is the interval \((-4,3) .\) Without actually performing any work, give the solution set of the inequality \(x^{2}+x-12 \geq 0\)

A student was asked to solve the quadratic equation \(x^{2}=16\) and did not get full credit for the solution set \(\\{4\\} .\) WHAT WENT WRONG?

A student claimed that the equation \(2 x^{2}-5=0\) cannot be solved using the quadratic formula because there is no first-degree \(x\) -term. Was the student correct? If not, give the values of \(a, b,\) and \(c\)

Identify the vertex of each parabola. $$ f(x)=\frac{1}{2} x^{2} $$

Use the zero-factor property to solve each equation. (Hint: In Exercises 9 and 10 , write the equation in standard form first. ) See Example 1 $$ x^{2}+3 x+2=0 $$

Identify the vertex of each parabola. $$ f(x)=x^{2}+4 $$

Use the quadratic formula to solve each equation. (All solutions for these equations are real numbers.) $$ x^{2}-8 x+15=0 $$

Use the zero-factor property to solve each equation. (Hint: In Exercises 9 and 10 , write the equation in standard form first. ) See Example 1 $$ x^{2}+8 x+15=0 $$

Use the quadratic formula to solve each equation. (All solutions for these equations are real numbers.) $$ x^{2}+3 x-28=0 $$