Answer:
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
