Answer:
The vertex form equation for the given graph is y = -(x - 2)² + 2
Explanation:
The vertex form of the quadratic equation is y = a(x - h)² + k, where
- a is the coefficient of x²
- (h, k) are the coordinates of the vertex point
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