2. Identify the vertex from the quadratic function y=-5(x-6)^2+8 *2 points(-5, 6)(-6,8)(6,8)(8,6

2) We are told to find the vertex of the quadratic function. The vertex of a quadratic function is the point at the base of the curve/graph of the function. It is the point where the value of the quadratic function changes sign.

The x-coordinate of this vertex is given as

x = (-b/2a)

The y-coordinate is then obtained from the value of the x-coordinate.

The quadratic function for the question is

y = -5 (x - 6)² + 8

We first need to put the quadratic function in the general form of

y = ax² + bx + c

So, we first simplify the expression

y = -5 (x - 6)² + 8

= -5 (x² - 12x + 36) + 8

= -5x² + 60x - 180 + 8

y = -5x² + 60x - 172

So,

a = -5

b = 60

c = -172

For the vertex

x = (-b/2a)

= [-60/(2×-5)]

= [-60/-10]

= 6

So, if x = 6.

y = -5x² + 60x - 172

y = -5(6²) + 60(6) - 172

y = -5(36) + 360 - 172

y = -180 + 360 - 172

y = 8

So, the vertex of the quadratic function is at

x = 6, y = 8.

In coordinate form, the vertex = (6, 8)

Option C is correct.

4) y = -3(x²)

The graph of x² is a parabola, but multiplying the function x² by -3 transforms the graph.

The 3, because it is greater than 1, stretches or enlarges the graph.

And the minus sign in front of the 3, ,that is, -3 reflects the graph about the x-axis.

So, altogether, -3 stretches the graph and reflects it about the x-axis.

Option A is correct.

Hope this Helps!!!