Quadratic Equations and Functions

In the following exercises, rewrite each function in the $f\left(x\right)=a(x-h{)}^2+k$ form by completing the square.

$f\left(x\right)=2x^2-12x+7$

Use the discriminant to determine the number and type of solutions of each quadratic equation.

$6p^2-13p+7=0$

Solve $x^2-48=0$

Solve $y^2-27=0$

Solve $2x^2=98$

Solve $5m^2=80$

Solve $c^2+12=0$

Solve $q^2+24=0$

Solve $\frac{1}{2}{x}^2+4=24$

Solve $\frac{3}{4}{y}^2-3=18$

Solve $5r^2-2=34$

Solve $3t^2+6=70$

Solve $3{(a-3)}^2=54$

Solve ${\left(x-\frac{1}{2}\right)}^2=\frac{5}{4}$

Solve ${\left(y+\frac{3}{4}\right)}^2=\frac{7}{16}$

Solve $5{(a-5)}^2+4=104$

Solve ${(3r+4)}^2=-8$

Solve ${(2t-8)}^2=-10$

Solve $9m^2-12m+4=25$

Solve $16n^2+40n+25=4$

Solve Quadratic Equations of the Form $a{x}^2=k$Using the Square Root Property.

In the following exercises, solve each equation $a^2=49$

Solve Quadratic Equations of the Form $a{x}^2=k$Using the Square Root Property.

In the following exercises, solve each equation $b^2=144$

Solve Quadratic Equations of the Form $a{x}^2=k$ Using the Square Root Property.

In the following exercises, solve each equation  $r^2-24=0$

Solve Quadratic Equations of the Form $a{x}^2=k$Using the Square Root Property.

In the following exercises, solve each equation $t^2-75=0$

Solve Quadratic Equations of the Form $a{x}^2=k$Using the Square Root Property.

In the following exercises, solve each equation $u^2-300=0$

Solve Quadratic Equations of the Form $a{x}^2=k$Using the Square Root Property.

In the following exercises, solve each equation $v^2-80=0$

Solve Quadratic Equations of the Form $a{x}^2=k$Using the Square Root Property.

In the following exercises, solve each equation $4m^2=36$

Solve Quadratic Equations of the Form $a{x}^2=k$

Using the Square Root Property.

In the following exercises, solve each equation $3n^2=48$

Solve Quadratic Equations of the Form $a{x}^2=k$Using the Square Root Property.

In the following exercises, solve each equation $\frac{4}{3}{x}^2=48$

Solve Quadratic Equations of the Form  $a{x}^2=k$Using the Square Root Property.

In the following exercises, solve each equation $\frac{5}{3}{y}^2=60$.

In the following exercises, solve each equation.

$x^2+25=0$

In the following exercises, solve each equation.

$y^2+64=0$

In the following exercises, solve each equation.

$x^2+63=0$

In the following exercises, solve each equation.

$y^2+45=0$

In the following exercises, solve each equation.

$\frac{4}{3}{x}^2+2=110$

In the following exercises, solve each equation.

$\frac{2}{3}{y}^2-8=-2$

In the following exercises, solve each equation.

$\frac{2}{5}{a}^2+3=11$

In the following exercises, solve each equation.

$\frac{3}{2}{b}^2-7=41$

In the following exercises, solve each equation.

$7p^2+10=26$

In the following exercises, solve each equation.

$2q^2+5=30$

In the following exercises, solve each equation.

$5y^2-7=25$

In the following exercises, solve each equation.

$3x^2-8=46$

In the following exercises, solve each equation.

${(u-6)}^2=64$

In the following exercises, solve each equation.

${(v+10)}^2=121$

In the following exercises, solve each equation.

${(m-6)}^2=20$

In the following exercises, solve each equation.

${(n+5)}^2=32$

In the following exercises, solve each equation.

${\left(r-\frac{1}{2}\right)}^2=\frac{3}{4}$

In the following exercises, solve each equation.

${\left(x+\frac{1}{5}\right)}^2=\frac{7}{25}$

In the following exercises, solve each equation.

${\left(y+\frac{2}{3}\right)}^2=\frac{8}{81}$

In the following exercises, solve each equation.

${\left(t-\frac{5}{6}\right)}^2=\frac{11}{25}$