The equation of a parabola is given.

y=−1/4x^2+4x−19

What are the coordinates of the vertex of the parabola?

Acceptfully
May 29, 2017

#1**+3 **

Here's one way to do it.

We can get the equation of this parabola in vertex form.

y = -1/4 x^{2} + 4x - 19

Multiply through by -4 .

-4y = x^{2} - 16x + 76

Subtract 76 from both sides of the equation.

-4y - 76 = x^{2} - 16x

Add (16/2)^{2} , or 64, to both sides of the equation.

-4y - 76 + 64 = x^{2} - 16x + 64

Now we can factor the right side.

-4y - 12 = (x - 8)^{2}

Divide both sides by -4.

(y + 3) = (-1/4) (x - 8)^{2}

Now we can see that the vertex of the parabola is the point (8 , -3 )

hectictar
May 29, 2017

#1**+3 **

Best Answer

Here's one way to do it.

We can get the equation of this parabola in vertex form.

y = -1/4 x^{2} + 4x - 19

Multiply through by -4 .

-4y = x^{2} - 16x + 76

Subtract 76 from both sides of the equation.

-4y - 76 = x^{2} - 16x

Add (16/2)^{2} , or 64, to both sides of the equation.

-4y - 76 + 64 = x^{2} - 16x + 64

Now we can factor the right side.

-4y - 12 = (x - 8)^{2}

Divide both sides by -4.

(y + 3) = (-1/4) (x - 8)^{2}

Now we can see that the vertex of the parabola is the point (8 , -3 )

hectictar
May 29, 2017