91Ó°ÊÓ

Without graphing, tell how many \(x\) -intercepts each function has. $$ y=3 x^{2}-10 x+6 $$

Without graphing, tell how many \(x\) -intercepts each function has. $$ y=10 x^{2}+13 x-3 $$

What can you add to \(x^{2}+5 x\) to get a perfect square trinomial? \(\begin{array}{llll}{\text { A. } \frac{25}{4}} & {\text { B. } \frac{25}{2}} & {\text { C. } 25} & {\text { D. } 2.5 x}\end{array}\)

Error Analysis After analyzing a quadratic equation with real coefficients, a student says that the equation has exactly one imaginary solution. Explain how you know that the student is wrong.

Physics Suppose you throw a ball straight up from the ground with a velocity of 80 \(\mathrm{ft} / \mathrm{s}\) . As the ball moves upward, gravity slows it. Eventually the ball begins to fall back to the ground. The height \(h\) of the ball after \(t\) seconds in the air is given by the quadratic function \(h(t)=-16 t^{2}+80 t .\) a. How high does the ball go? b. For how many seconds is the ball in the air before it hits the ground?

Solve \(14 x=x^{2}+36 .\) Show your work.

For each function, the vertex of the function's graph is given. Find \(a\) and \(b\) \ $$ y=a x^{2}+b x+5 ;(-1,4) $$

Factor each expression completely. $$ 3600 z^{2}-4900 $$

Use the Quadratic Formula to prove each statement. a. The sum of the solutions of the quadratic equation \(a x^{2}+b x+c=0\) is \(-\frac{b}{a}\) b. The product of the solutions of the quadratic equation \(a x^{2}+b x+c=0\) is \(\frac{c}{a}\)

What is the number \(\sqrt{-225}+36\) when written in the form \(a+b i ?\) $$\begin{array}{llll}{\text { A. }-15+6 i} & {\text { B. } 6+15 i} & {\text { C. } 6-15 i} & {\text { D. } 36+15 i}\end{array}$$