Question

Write the equation of the quadratic function given vertex V and point P, which lies on the function. Write the equation in standard form f(x) = ax ^ 2 + bx + c; (4, 3); P(- 4,131)

Answer 1

f(x) = 2x^2 - 16x + 35

Explanation:

To find the equation of the quadratic function, we need the vertex V and a point P that lies on the function.

Given:

Vertex V: (4, 3)

Point P: (-4, 131)

The vertex form of a quadratic function is given by:

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

Where (h, k) represents the vertex.

Using the vertex V (4, 3), we have:

h = 4

k = 3

Substituting these values, we get:

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

Now, we can use the point P(-4, 131) to find the value of 'a'.

Substituting x = -4 and y = 131 into the equation:

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

131 = a(-8)^2 + 3

131 = a * 64 + 3

131 - 3 = 64a

128 = 64a

a = 128 / 64

a = 2

Now, substituting the value of 'a' back into the equation:

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

Expanding and simplifying:

f(x) = 2(x^2 - 8x + 16) + 3

f(x) = 2x^2 - 16x + 32 + 3

f(x) = 2x^2 - 16x + 35

Therefore, the equation of the quadratic function in standard form, with vertex (4, 3) and passing through point (-4, 131), is:

f(x) = 2x^2 - 16x + 35