Question

For the following exercises, use the vertex (h, k) and a

point on the graph (x,y) to find the general (expanded)
form of the equation of the quadratic function. If your
answer is not an integer please round to the nearest
hundredth.
Our vertex (h, k) is (−2, −1)
Our point (x, y) on the graph is (-4,3)
the general (expanded) form is: f(x) = ax²+bx+c
where:
A=
B=
C=

Answer 1

To find the equation of the quadratic function, we can use the vertex form of the equation, which is:

f(x) = a(x - h)^2 + k

where (h, k) is the vertex. Plugging in the values we have:

f(x) = a(x - (-2))^2 - 1

Simplifying:

f(x) = a(x + 2)^2 - 1

Now we can use the point (-4, 3) to solve for a:

3 = a(-4 + 2)^2 - 1

3 = 4a - 1

4a = 4

a = 1

Therefore, the equation of the quadratic function in general form is:

f(x) = x^2 + 4x + 3

So, A = 1, B = 4, and C = 3.