Answer: a) y = 2(x + 3)² - 7
b) y = -2(x + 4)² + 6
c) y = 3(x - 7)² + 4
<u>Step-by-step explanation:</u>
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 any point on the curve
Input (h, k) and (x, y) to solve for "a"
a) (h, k) = (-3, 7) and (x, y) = (-2, -5)
-5 = a(-2 + 3)² - 7
2 = a(1)²
2 = a
<h2>
y = 2(x + 3)² - 7</h2>
b) (h, k) = (1, 3) and (x, y) = (2, 5)
5 = a(2 - 1)² + 3
2 = a(1)²
2 = a
<h2>
y = 2(x - 1)² + 3</h2>
c) (h, k) = (-4, 6) and (x, y) = (-2, -2)
-2 = a(-2 + 4)² + 6
-8 = a(2)²
-8 = 4a
-2 = a
<h2>
y = -2(x + 4)² + 6</h2>
d) (h, k) = (7, 4) and (x, y) = (5, 16)
16 = a(5 - 7)² + 4
12 = a(-2)²
12 = 4a
3 = a
<h2>
y = 3(x - 7)² + 4</h2>