Complete the square to re-write the quadratic function in vertex form: y=x^(2)+8x-9 Answer: y=

Question

Complete the square to re-write the quadratic function in vertex form:  y=x^(2)+8x-9 Answer:  y=

Bytelearn · Accepted Answer

Identify Vertex Form: Identify the vertex form of a parabola. The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Begin with Quadratic Function: Begin with the given quadratic function. We have the quadratic function y = x^2 + 8x - 9.Separate Constant Term: Separate the constant term from the x terms. To complete the square, we need to isolate the x terms. So we write the function as y = (x^2 + 8x) - 9.Find Completing Number: Find the number to complete the square. To complete the square, we need to add and subtract the square of half the coefficient of x inside the parentheses. The coefficient of x is 8, so half of it is 4, and the square of 4 is 16. We will add and subtract 16 inside the parentheses.Add/Subtract Square: Add and subtract the square of half the coefficient of x inside the parentheses. We write the function as y = (x^2 + 8x + 16) - 16 - 9.Factor and Simplify: Factor the perfect square trinomial and simplify the constants. The expression x^2 + 8x + 16 is a perfect square trinomial and can be factored as (x + 4)^2. The constants -16 and -9 combine to -25. So the function becomes y = (x + 4)^2 - 25.Write Final Vertex Form: Write the final vertex form of the quadratic function. The vertex form of the quadratic function is y = (x + 4)^2 - 25.

Complete the square to re-write the quadratic function in vertex form: $\newline$ $y=x^{2}+8 x-9$ $\newline$ Answer: $y=$

Full solution

More problems from Convert equations of parabolas from general to vertex form

Related topics

Complete the square to re-write the quadratic function in vertex form:\newliney=x2+8x−9 y=x^{2}+8 x-9 y=x2+8x−9\newlineAnswer: y= y= y=

Complete the square to re-write the quadratic function in vertex form: $\newline$ $y=x^{2}+8 x-9$ $\newline$ Answer: $y=$