Question

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left parenthesis, x, comma, y, right parenthesis(x,y) point.
y, equals, minus, 4, x, squared, plus, 8
y=−4x
2
+8

Answer 1

To find the vertex of the parabola given by the equation \( y = -4x^2 + 8 \), we can use the formula for the vertex of a parabola in the standard form \( y = ax^2 + bx + c \). The x-coordinate of the vertex can be found using the formula:

\[
x = -\frac{b}{2a}
\]

In your equation \( y = -4x^2 + 8 \), we have:

- \( a = -4 \)
- \( b = 0 \) (since there is no linear \( x \) term)
- \( c = 8 \)

Now, substituting \( a \) and \( b \) into the vertex formula:

\[
x = -\frac{0}{2(-4)} = 0
\]

Now we can find the y-coordinate of the vertex by substituting \( x = 0 \) back into the equation:

\[
y = -4(0)^2 + 8 = 8
\]

Thus, the coordinates of the vertex are:

\[
(0, 8)
\]

Therefore, the vertex of the parabola is \(\boxed{(0, 8)}\).