Completing the square to vertex form Quiz 1

Question 1

Find the vertex form of the equations $$3{{x}^{2}}-3x+9=y$$

Accepted Answer

$$4y-33=12{{\left( x-\dfrac{1}{2} \right)}^{2}}$$

Answer

$$2y+3x=3{{\left( x-\dfrac{1}{2} \right)}^{2}}$$

Answer

$$2y+3=3\left( x-\dfrac{1}{2} \right)$$

Answer

$$4y-33=12{{\left( x-1 \right)}^{2}}$$

Question 2

Form the vertex form, from the quadratic equation $$-2{{x}^{2}}+x-5=y$$

Accepted Answer

$$8y+39=-16{{\left( x-\dfrac{1}{4} \right)}^{2}}$$

Answer

$$8y+38=16{{\left( x-\dfrac{1}{4} \right)}^{2}}$$

Answer

$$8y-39=16{{\left( x+\dfrac{1}{4} \right)}^{2}}$$

Answer

None

Question 3

Derive the quadratic equation from $$\left( y-7 \right)=-{{\left( x-2 \right)}^{2}}$$ and find $$h$$ and $$k$$.

Accepted Answer

$$-{{x}^{2}}+4x+3,h=2,k=7$$

Answer

$${{x}^{2}}-4x+3,h=2,k=7$$

Answer

$${{x}^{2}}+4x-3,h=-2,k=-7$$

Answer

None

Question 4

Derive the quadratic equation from $$y+9=2{{\left( x-1 \right)}^{2}}$$ and find $$h,k$$.

Accepted Answer

$$2{{x}^{2}}-4x-7=y,h=1,k=-9$$

Answer

$$2{{x}^{2}}+4x+7=y,h=1,k=9$$

Answer

$$-2{{x}^{2}}+4x+7=y,h=-1,k=9$$

Answer

None

Question 5

Find the vertex form of the equation $$6{{x}^{2}}+2x+21=y$$

Accepted Answer

$$6y-36{{\left( x+\dfrac{1}{6} \right)}^{2}}-125=0$$

Answer

$$6y-123=36{{\left( x+\dfrac{1}{6} \right)}^{2}}$$

Answer

$$y+\dfrac{123}{6}=6{{\left( x+\dfrac{1}{6} \right)}^{2}}$$

Answer

None