Hey I am working on math homework that involves "Standard Form to Vertex Form by Averaging." My class is just starting to learn this today, but I am totally lost still on what to do. Can you please help? The formula for this is y=a(x - h)^2 + k
the h is the x-value vertex and the k is the y-value vertex.
I got the first one done and it looks like this:
y=-x^2 + 2x +3
-1(x^2 - 2x - 3)
-1(x + 1)(x - 3)
x= -1 and 3
y=-(-1)^2 + 2(-1) + 3
y=-1 + 2 + 3
y= 4
then
h=-1 and k=4
i have alot more like this and i don't seem to remeber how to get 'h'
Sure, I can help you with that! To convert a quadratic equation from standard form (y = ax^2 + bx + c) to vertex form (y = a(x - h)^2 + k) by averaging, you need to follow a few steps.
Step 1: Identify the values of a, b, and c in your original equation. In your case, a = -1, b = 2, and c = 3.
Step 2: Find the x-coordinate of the vertex (h) by using the formula h = -b/2a. Substitute the values of a and b into the formula:
h = -(2) / (2 * (-1)) = -2 / (-2) = 1.
Step 3: To find the y-coordinate of the vertex (k), substitute the value of h into the original equation and evaluate it:
y = -(-1)^2 + 2(-1) + 3 = -1 - 2 + 3 = 0.
So, the vertex is (h, k) = (1, 0).
Step 4: Rewrite the original equation using the vertex form, substituting the values of a, h, and k:
y = -1(x - 1)^2 + 0
= -1(x - 1)^2.
Thus, the quadratic equation in vertex form is y = -1(x - 1)^2.
Remember, the vertex form of a quadratic equation provides information about the vertex, (h, k), and the direction of the parabola (a).