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# Help, Parabolas

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The equation of a parabola is given.

y=−1/4x^2+4x−19

What are the coordinates of the vertex of the parabola?

May 29, 2017

#1
+7352
+3

Here's one way to do it.

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

y = -1/4 x2 + 4x - 19

Multiply through by -4 .

-4y = x2 - 16x + 76

Subtract 76 from both sides of the equation.

-4y - 76 = x2 - 16x

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

-4y - 76 + 64 = x2 - 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 )

May 29, 2017

#1
+7352
+3

Here's one way to do it.

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

y = -1/4 x2 + 4x - 19

Multiply through by -4 .

-4y = x2 - 16x + 76

Subtract 76 from both sides of the equation.

-4y - 76 = x2 - 16x

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

-4y - 76 + 64 = x2 - 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