MATH SOLVE

5 months ago

Q:
# Can someone explain to me how to find the vertex form of this equation?y= -x^2 + 12x-4Do i use the -b/2a formula? I just need this to be explained better biased on a equation i need to solve.

Accepted Solution

A:

The quadratic equation has the general formula:

y = ax^2 + bx + c

The vertex form has the general formula:

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

To get the vertex formula, we will need to get the values of a,h and k as follows:

1- The value of a:

The value of "a" in the vertex form is the same as the value of "a" in the quadratic form

Therefore: a = -1

2- The value of h:

the value of "h" can be computed using the formula:Β

h = -b / 2a

From the given quadratic equation: b = 12 and a = -1

Therefore: h = -12 / 2(-1) = 12/2 = 6

3- The value of k:

The value of k can be computed easily by evaluating y at the calculated h as follows:

The given equation is: y = -x^2 + 12x - 4

Compute the result at x=h=6 to get k as follows:

k = y = -(6)^2 + 12(6) - 4 = 32

Therefore, based on the above calculations, the vertex form would be:

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

y = -(x-6)^2 + 32

y = ax^2 + bx + c

The vertex form has the general formula:

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

To get the vertex formula, we will need to get the values of a,h and k as follows:

1- The value of a:

The value of "a" in the vertex form is the same as the value of "a" in the quadratic form

Therefore: a = -1

2- The value of h:

the value of "h" can be computed using the formula:Β

h = -b / 2a

From the given quadratic equation: b = 12 and a = -1

Therefore: h = -12 / 2(-1) = 12/2 = 6

3- The value of k:

The value of k can be computed easily by evaluating y at the calculated h as follows:

The given equation is: y = -x^2 + 12x - 4

Compute the result at x=h=6 to get k as follows:

k = y = -(6)^2 + 12(6) - 4 = 32

Therefore, based on the above calculations, the vertex form would be:

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

y = -(x-6)^2 + 32