Answer: (a) y = -7(x - 1)² + 2
(b) y = 4/9(x - 3)² + 6
(c) y = -7x² + 5
Explanation:
The vertex form of a quadratic equation is: y = a(x - h)² + k where
- "a" is the vertical stretch
- (h, k) is the vertex
- (x, y) is a point on the parabola
Input the vertex (h, k) and the point (x, y) into the equation to solve for "a"
(a) Vertex (h, k) = (1, 2) Point (x, y) = (2, -5)
y = a(x - h)² + k
↓ ↓ ↓ ↓
-5 = a(2 - 1)² + 2
-7 = a(1)²
-7 = a
y = -7(x - 1)² + 2
(b) Vertex (h, k) = (3, 6) Point (x, y) = (0, 2)
y = a(x - h)² + k
↓ ↓ ↓ ↓
2 = a(0 - 3)² + 6
-4 = a(-3)²
-4 = -9a
4/9 = a
y = -4/9(x - 3)² + 6
(c) Vertex (h, k) = (0, 5) Point (x, y) = (1, -2)
y = a(x - h)² + k
↓ ↓ ↓ ↓
-2 = a(1 - 0)² + 5
-7 = a(1)²
-7 = a
y = -7(x - 0)² + 5