SOLUTION: a.) Write the equation below in factored form and identify its x-intercepts. y=x^2+12x+35 b.) Now write the equation in vertex form. c.)now sketch the graph

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: a.) Write the equation below in factored form and identify its x-intercepts. y=x^2+12x+35 b.) Now write the equation in vertex form. c.)now sketch the graph      Log On


   

Question 968373: a.) Write the equation below in factored form and identify its x-intercepts.
y=x^2+12x+35
b.) Now write the equation in vertex form.
c.)now sketch the graph
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(a):

Factorize the right-hand member and you have the factored form.
y=%28x%2B5%29%28x%2B7%29;
You also see directly from this that the roots are -5 and -7.

(b):

Complete the Square for the quadratic right-hand expression. See your textbook's lesson on this or study the lesson available here: http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev.

Your term to use is %2812%2F2%29%5E2=6%5E2.

x%5E2%2B12x%2B35
x%5E2%2B12x%2B6%5E2%2B35-6%5E2
%28x%2B6%29%5E2%2B35-36
highlight%28y=%28x%2B6%29%5E2-1%29

You can compare how the two forms of equation appear. The standard form, found after completing the square, lets you read the vertex directly from the equation. Vertex is a minimum, at (-6,-1).

Graph the equation?
You have the vertex, you know it is a minimum, and you have the two roots. You can graph this.