Write an equation for a quadratic function that has a vertex of (-4,0) and the parabola passes through the point (-6,12)

Answer 1

y = a(x - h)² + k, where (h, k) is the vertex

y = a(x + 4)² + 0

Since (-6,12) is on the graph, we have 12 = a(-6 + 4)².

12 = 4a So, a = 3.

Equation in vertex form is y = 3(x + 4)²

Simplifying, we get y = 3x² + 24x + 48.

Answer 2

Strategy for writing a quadratic function:

1. Find a useful formula.
2. In this case, vertex form is useful: y = a(x - h)² + k
3. Identify what's needed and what's given.
4. We need a, h and k so we can write a function using only x and y.
5. We are given a vertex (-4, 0), which is (h, k)
6. We are given another point (-6, 12), which is (x, y)
7. We now need to solve for a.
8. Plug in.
9. y = a(x - h)² + k becomes 12 = a(-6 - -4)² + 0
10. Simplify and solve.
11. 12 = a(-6 - -4)² + 0
12. 12 = a(-6 + 4)²
13. 12 = a(-2)²
14. 12 = a·4
15. 3 = a
16. Notice that you have everything you needed (a, h and k) and answer the question.
17. Write the quadratic function in vertex form (replacing a, h and k with their values, and leaving x and y in the equation): y = 3(x+4)²

Answer 3

Hey Grant! These types of questions used to frustrate me in high school too but they turned out to be the easiest! Follow this secret recipe to reach the answer in the simplest possible manner!

1. The vertex form for a quadratic function --> y=a(x-h)^2+k
2. Vertex --> (h,k) --> (-4,0)
3. "Passes through the point (-6,12) --> (x,y) --> (-6,12)
4. 12=a(-6+4)^2+0 --> 12=4a+0 --> 4a=12 --> a=12/4 --> a=3
5. Since "a" is positive, then the parabola opens Upwards
6. So, the equation for the quadratic function in the vertex form is y=3(x+4)^2
7. If we distribute the bracket, we can get to the Standard Form for the quadratic function
8. y=3(x^2+8x+16) --> y=3x^2+24x+48

This is it, Grant! Remember, I offer my online tutoring sessions at a very competitive rate of $25/hr and I am always happy to adjust to your availability!