What is the Vertex form of the equation
y=x^2+4x-3
y = x^2+4x-3
complete the square: add and subtract 4
y = x^2+4x+4 - 3 - 4
y = (x+2)^2 - 7
Thanks
To express the equation y = x^2 + 4x - 3 in vertex form, we need to complete the square. Here's how to do it step by step:
Step 1: Group the terms with x^2 and x together.
y = (x^2 + 4x) - 3
Step 2: Take half the coefficient of x (which is 4) and square it.
1/2 * 4 = 2
2^2 = 4
Step 3: Add and subtract the value obtained in Step 2 inside the parentheses.
y = (x^2 + 4x + 4 - 4) - 3
Step 4: Rearrange the equation to group the perfect square trinomial with x^2.
y = ((x^2 + 4x + 4) - 4) - 3
Step 5: Simplify the equation inside the parentheses.
y = (x + 2)^2 - 7
Now we have the equation in vertex form: y = (x + 2)^2 - 7.
The vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex. In our case, the vertex is (-2, -7).