Write the vertex form equation for the graph shown.

The vertex form equation for the given graph is y = -(x - 2)² + 2

Step-by-step explanation:

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

From the given figure

∵ The graph is a parabola the graph of the quadratic equation

∵ Its maximum point is (2, 2)

∴ Its vertex is (2, 2)

→ By using the facts above

∴ h = 2 and k = 2

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

∴ y = a(x - 2)² + 2

→ To find a substitute x and y in the equation by a point on the curve

∵ The point (0, -2) lies on the parabola

∴ x = 0 and y = -2

→ Substitute them in the equation

∵ -2 = a(0 - 2)² + 2

∴ -2 = a(-2)² + 2

∴ -2 = a(4) + 2

∴ -2 = 4a + 2

→ Subtract 2 from both sides

∴ -4 = 4a

→ Divide both sides by 4

∴ -1 = a

→ Substitute it in the equation above

∴ y = -1(x - 2)² + 2

∴ y = -(x - 2)² + 2

∴ The vertex form equation for the given graph is y = -(x - 2)² + 2

x=half

step-by-step explanation: