+128 The equation of a parabola is given.
y=−1/4x^2+4x−19
What are the coordinates of the vertex of the parabola?
+9466 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 )
+9466 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 )
