Start by identifying a, b, and c. Then use the expression - b2a to find the x-coordinate of the vertex.
y=(x+3)^2-7
Practice makes perfect
We have a quadratic function written in standard form, and we want to rewrite it in vertex form.
Standard Form:& y= ax^2+ bx+c
Given Equation:& y= 1x^2+ 6x+2
In the given equation, a= 1, b= 6, and c=2.
Let's now recall the vertex form of a quadratic function.
Vertex Form: y=a(x-h)^2+k
In this equation, a is the leading coefficient of the quadratic function, and the point (h,k) is the vertex of the parabola. By substituting our given values for a and b into the expression - b2a, we can find h.
Therefore, the (h,k) coordinate pair of the vertex is (-3,-7). Moreover, since we already know that a= -2, we can rewrite the given function in vertex form.
y= 1 (x-(-3))^2+(-7)
⇔ y = (x+3)^2-7
