Chapter 9

Decide whether the parabola opens up or down. $$ y=-6 x^{2}-15 x $$

Use a graph to estimate the solutions of the equation. Check your solutions algebraically. $$x^{2}+2 x=3$$

Write the equation in standard form. Identify the values of a, b, and c. $$3 x^{2}=27 x$$

Determine whether the equation has two solutions, one solution, or no real solution. \(x^{2}-3 x+2=0\)

Simplify the expression. $$ \sqrt{54} $$

Solve the equation or write no real solution. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ y^{2}=15 $$

Write the equation in words. $$ \sqrt{49}=7 $$

Sketch the graph of the function. Plot the given point and determine whether the point lies inside or outside the parabola. $$ \begin{aligned} &y=\frac{1}{2} x^{2}+x-4\\\ &C(1,0) \end{aligned} $$

Decide whether the parabola opens up or down. $$ y=8 x-x^{2} $$

Use a graph to estimate the solutions of the equation. Check your solutions algebraically. $$-4 x^{2}-8 x=-12$$

Write the equation in standard form. Identify the values of a, b, and c. $$-24 x+45=-3 x^{2}$$

Determine whether the equation has two solutions, one solution, or no real solution. \(2 x^{2}-4 x+3=0\)

Simplify the expression. $$ \sqrt{18} $$

Solve the equation or write no real solution. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ x^{2}=225 $$

Write the equation in words. $$ \sqrt{1}=1 $$

Sketch the graph of the function. Plot the given point and determine whether the point lies inside or outside the parabola. $$ \begin{aligned} &y=4 x^{2}-x+1\\\ &D(-2,5) \end{aligned} $$

Find the coordinates of the vertex. Make a table of values, using \(x\) -values to the left and to the right of the vertex. $$ y=3 x^{2} $$

Use a graph to estimate the solutions of the equation. Check your solutions algebraically. $$-x^{2}+3 x=-4$$

Write the equation in standard form. Identify the values of a, b, and c. $$32-4 m^{2}=28 m$$

Determine whether the equation has two solutions, one solution, or no real solution. \(-3 x^{2}+5 x-1=0\)

Simplify the expression. $$ \sqrt{56} $$

Solve the equation or write no real solution. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ r^{2}=-81 $$

Write the equation in words. $$ \sqrt{\frac{1}{9}}=\frac{1}{3} $$

Complete the statement with always, sometimes, or never. If \(a>b,\) then \(a^{2}\) is ? greater than \(b^{2}\)

Find the coordinates of the vertex. Make a table of values, using \(x\) -values to the left and to the right of the vertex. $$ y=6 x^{2} $$

Use a graph to estimate the solutions of the equation. Check your solutions algebraically. $$2 x^{2}+4 x=6$$

Determine whether the equation has two solutions, one solution, or no real solution. \(2 x^{2}+3 x-2=0\)

Simplify the expression. $$ \sqrt{27} $$

Evaluate the expression. Check the results by squaring each root. $$ \sqrt{144} $$

Solve the equation or write no real solution. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ x^{2}=121 $$

Complete the statement with always, sometimes, or never. If \(a>b\) and \(b>0,\) then \(a^{2}\) is ? greater than \(b^{2}\)

Find the coordinates of the vertex. Make a table of values, using \(x\) -values to the left and to the right of the vertex. $$ y=-12 x^{2} $$

Use a graph to estimate the solutions of the equation. Check your solutions algebraically. $$3 x^{2}+3 x=6$$

Write the equation in standard form. Identify the values of a, b, and c. $$2 x^{2}-\frac{1}{5}=-\frac{2}{5} x$$

Determine whether the equation has two solutions, one solution, or no real solution. \(x^{2}-2 x+4=0\)

Simplify the expression. $$ \sqrt{63} $$

Evaluate the expression. Check the results by squaring each root. $$ \pm \sqrt{25} $$

Solve the equation or write no real solution. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ t^{2}=39 $$

Find the coordinates of the vertex. Make a table of values, using \(x\) -values to the left and to the right of the vertex. $$ y=2 x^{2}-10 x $$

Use a graph to estimate the solutions of the equation. Check your solutions algebraically. $$x^{2}-4 x-5=0$$

Write the equation in standard form. Identify the values of a, b, and c. $$\frac{1}{3}-2 x=\frac{2}{3} x^{2}$$

Determine whether the equation has two solutions, one solution, or no real solution. \(6 x^{2}-2 x+4=0\)

Simplify the expression. $$ \sqrt{200} $$

Evaluate the expression. Check the results by squaring each root. $$ \sqrt{196} $$

Solve the equation or write no real solution. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ x^{2}=256 $$

Complete the statement with always, sometimes, or never. If \(a\) is a real number, then \(\sqrt{a^{2}}\) is ? equal to \(|a|\)

Find the coordinates of the vertex. Make a table of values, using \(x\) -values to the left and to the right of the vertex. $$ y=-7 x^{2}+2 x $$

Use a graph to estimate the solutions of the equation. Check your solutions algebraically. $$x^{2}-x=12$$

Find the value of \(b^{2}\)- 4ac for the equation. $$x^{2}-3 x-4=0$$

Determine whether the equation has two solutions, one solution, or no real solution. \(3 x^{2}-6 x+3=0\)