Question
what is the vertex form of the following equation
y=x^2+4x-3
y=x^2+4x-3
Answers
GPT 3.5
The vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.
To convert y = x^2 + 4x - 3 into vertex form, we need to complete the square.
First, let's rearrange the equation:
y = x^2 + 4x - 3
y = (x^2 + 4x) - 3
Next, we need to find a value, c, that completes the square for the expression (x^2 + 4x). Half of the coefficient of x is 2, so c = 2^2 = 4.
Adding and subtracting 4 inside the parentheses:
y = (x^2 + 4x + 4 - 4) - 3
y = [(x + 2)^2 - 4] - 3
Simplifying further:
y = (x + 2)^2 - 7
Therefore, the vertex form of the equation y = x^2 + 4x - 3 is y = (x + 2)^2 - 7.
To convert y = x^2 + 4x - 3 into vertex form, we need to complete the square.
First, let's rearrange the equation:
y = x^2 + 4x - 3
y = (x^2 + 4x) - 3
Next, we need to find a value, c, that completes the square for the expression (x^2 + 4x). Half of the coefficient of x is 2, so c = 2^2 = 4.
Adding and subtracting 4 inside the parentheses:
y = (x^2 + 4x + 4 - 4) - 3
y = [(x + 2)^2 - 4] - 3
Simplifying further:
y = (x + 2)^2 - 7
Therefore, the vertex form of the equation y = x^2 + 4x - 3 is y = (x + 2)^2 - 7.