what is the vertex form of the equation
y=x^2+4x-3
Could someone please explain.
y = x^2 + 4x - 3
y = x^2 + 4x + 4 - 3 - 4
y = (x+2)^2 - 7
(y+7) = (x+2)^2
the vertex is at (-2,-7)
Thank you.
To find the vertex form of the equation y = x^2 + 4x - 3, we need to complete the square. The vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.
1. Start with the quadratic equation: y = x^2 + 4x - 3.
2. Complete the square by adding and subtracting the square of half the coefficient of x. In this case, the coefficient is 4, so we add and subtract (4/2)^2 = 4.
y = x^2 + 4x + 4 - 4 - 3.
3. Rearrange the equation to group the squared term with the x term:
y = (x^2 + 4x + 4) - 7.
4. Simplify the expression within the parentheses by factoring the quadratic trinomial:
y = (x + 2)^2 - 7.
5. Now, the equation is in vertex form. The vertex is given by the coordinates (-2, -7).
Therefore, the vertex form of the equation y = x^2 + 4x - 3 is y = (x + 2)^2 - 7.