I am having a math crises and I have a test tomorrow and nothing is sinking in can someone please help me out

Question

here is the problem
rewrite the quadratic function in the vertex form y=a(x-p)squared+q

Here is the question
1. y+x squared-4x-5

Answer 1

I'll illustrate the general procedure first:
y = ax^2 + bx + c
= a(x^2 + b/a x) + c
= a((x + b/2a)^2 - (b/2a)^2) + c
= a (x + b/2a)^2 + (c - b^2/4a)

For example:
y = 2x^2 - 3x + 7
= 2(x^2 - 3/2 x) + 7
= 2((x - 3/4)^2 - (3/4)^2) + 7
= 2(x-3/4)^2 - 2(9/16) + 7
= 2(x-3/4)^2 + 47/8.

In your case we have
y = x^2 - 4x - 5
Since the coefficient of x^2 is 1, we can skip the first bit.
y = (x-2)^2 - 2^2 - 5
=> y = (x-2)^2 - 9.

Answer 2

Is this an equation?

If it is, then y = -x**2 + 4x + 5

Remember that this is a parabola. Find the roots, there are the x intercepts if there are some. Find the y intercept, this is the independant term (5)

The axis is x = - b/2a, in this case, a = -1 , b = 4, and c = 5

Hope this helps


Good luck with your test!!!

Ana.