Find the equation of the quadratic function in vertex form, with vertex (-1, 8) that has a y- intercept of 4 (which means it passes through the point (0,4)).

The equation of the quadratic function is y = -4(x + 1)² + 8

Step-by-step explanation:

The vertex form of the quadratic function is y = a(x - h)² + k, where

∵ The vertex of the graph of the quadratic function is (-1, 8)

∴ h = -1 and k = 8

→ Substitute the values of h, k in the form of the equation above

∵ y = a(x - -1)² + 8

∴ y = a(x + 1)² + 8

→ To find a substitute x and y of the equation by the coordinates

   of a point lies on the graph of the function

∵ The y-intercept is 4

→ That means the graph intersect the y-axis at point (0, 4)

∴ x = 0 and y = 4

∵ 4 = a(0 + 1)² + 8

∴ 4 = a(1)² + 8

∴ 4 = a(1) + 8

∴ 4 = a + 8

→ Subtract 8 from both sides

∵ 4 - 8 = a + 8 - 8

∴ -4 = a

→ Substitute the value of a in the equation

∴ y = -4(x + 1)² + 8

∴ The equation of the quadratic function is y = -4(x + 1)² + 8

-6 is the correct option from the above given options