The vertex of this quadratic equation is (-7, 11), as option D. is the correct choice.
How do determine the vertex of a quadratic equation?
The vertex of a quadratic equation, considering the equation to be in the standard form:
y = ax² + bx + c,
is given by (x = -b/2a, y = (4ac - b²)/4a).
How do we determine the vertex of the given quadratic equation?
Given equation: h(x) = -5(x+7)² + 11
Solving it to the standard form:
h(x) = -5(x² + 14x + 49) + 11
⇒ h(x) = -5x² - 70x -245 + 11 = -5x² - 70x - 234.
When this equation is compared with the standard equation, we get
a = -5, b= -70, c = -234
Substituting the values in the formula of the vertex,
Vertex = ( -b/2a, (4ac - b²)/4a)
x coordinate = -(-70)/2(-5) = -7
y coordinate = ( 4(-5)(-234) - (-70²))/4(-5) = (4680 - 4900)/(-20) = -220/-20 = 11
∴ Vertex = (-7, 11)
Learn more about Vertex of the quadratic equation at
https://brainly.com/question/3363463
#SPJ2
