Help Math. Can you help me with the following problem?

Question

Ok, so i have a math exam tomorrow and i know my stuff pretty well but for some reason i am blanking on how to do this...

write an equation for the quadratic function whose graph contains the given vertex and point

Vertex, (-2, -3) point (1,2)

I know that the equation is y=(5/9)(x+2)^2 -3. But what formula do i have to use to get to this equation?

Point guaranteed if you show me how to do it

Answer 1

Use the equation for a parabola:

**y = a (x - h) + k, where (h, k) is the vertex of the parabola.

You have h and k: h = -2, k = -3. Just substitute the given x and y values from the point (1, 2) into the starred equation above, and then solve for a. That gives the last element needed to define the entire equation.

2 = a (1 + 2)² - 3
5 = 9 a
5/9 = a

Substituting these values into the equation y = a (x - h) + k, we get:

y = 5/9 (x + 2)² - 3.

Answer 2

Use the equation y=k(x-a)^2+b where the vertex is (a,b) and k is a constant

If you have the vertex (-2,-3) , then a= -2 and b= -3

Plug that back into the equation to get

y=k(x-(-2))^2+(-3)
y=k(x+2)^2-3

Now you are given the point (1,2) so you plug that in for x and y to get

2=k(1+2)^2-3

Now solve for k
2=k(3)^2-3
2=9k-3
5=9k
5/9=k

so the equation is:

y=(5/9)(x+2)^2+3

Answer 3

The vertex of y = kx^2 is (0,0).
To make the vertex (a, b), the curve needs to move a units to the right and b units up.
You therefore replace the y in y = kx^2 with y - b and the x with x - a.
That gives you y - b = k(x - a)^2 ..........(1)
To ensure the graph passes through (p, q), put x = p and y = q in (1), and solve for k:
q - b = k(p - a)^2
k = ( q - b ) / (p - a)^2 ........(2)

For your parabola, put a = -2, b = -3 in (1) and (2).
Solve (2) for k, and then substitute that in (1).

I would advise you learn the technique rather than the final formula.

Answer 4

quadratic formula is -b + or - square root of b^2 - 4(a)(c) all over 2(a). i hope it helps

Answer 5

that's the equation for slopes
so you should do the standard equation for slopes.

Answer 6

: - 0