What is the vertex form of y=13x^2 +3x- 36 ?
1 Answer
vertex form:
Explanation:
1. Factor 13 from the first two terms.
y=13x^2+3x-36
y=13(x^2+3/13x)-36
2. Turn the bracketed terms into a perfect square trinomial.
When a perfect square trinomial is in the form
y=13(x^2+3/13x+(3/13x-:2)^2)-36
y=13(x^2+3/13x+9/676)-36
3. Subtract 9/676 from the perfect square trinomial.
You cannot just add
y=13(x^2+3/13x+9/676 color(red)(-9/676))-36
4. Multiply -9/676 by 13.
The next step is to bring
y=color(blue)13(x^2+3/13x+9/676)-36[color(red)((-9/676))*color(blue)((13))]
5. Simplify.
y=(x^2+3/13x+9/676)-36-9/52
y=(x^2+3/13x+9/676)-1881/52
6. Factor the perfect square trinomial.
The last step is to factor the perfect square trinomial. This will allow you to determine the coordinates of the vertex.
color(green)(y=(x+3/26)^2-1881/52)