Question

Complete the general form equation of the parabola that passes through (4,101) with vertex at (−3,3) .

f(x)=

Answer 1

f(x) = 2x²+12x+21

Explanation:

1. Start with Vertex Form: y = a(x-h)²+k; Vertex (h,k)=(-3,3):

y = a(x + 3)²+3

2. Replace x and y with (x,y)=(4,101) in your step 1 equation:

101 = a(4+3)²+3

3. Simplify the right side and solve for a:

101 = 49a+3

49a = 98

a = 2

4. Replace a with 2 in your step 1 equation:

y = a(x + 3)²+3 ⇒ y = 2(x + 3)²+3

5. Follow Order of Operations to convert step 4 equation to Standard Form: (x + 3)² = x²+6x+9

2(x²+6x+9) = 2x²+12x+18

2x²+12x+18 + 3 = 2x²+12x+21