SOLUTION: Please find the standard form/vertex form, vertex, x-intercept and y-intercept, and the graph of this function h(x)= -4x^2-8x+3

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Please find the standard form/vertex form, vertex, x-intercept and y-intercept, and the graph of this function h(x)= -4x^2-8x+3      Log On


   

Question 825023: Please find the standard form/vertex form, vertex, x-intercept and y-intercept, and the graph of this function h(x)= -4x^2-8x+3
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This relies on Completing the Square. This kind of question happens often.

Factor the -4 from the entire right-hand expression:
h%28x%29=-4%28x%5E2%2B2x-3%2F4%29
The terms containing x in the quadratic expression in the parentheses represents a square with the area %282%2F2%29%5E2=1 missing. We ADD and SUBTRACT this inside the parentheses.
h%28x%29=-4%28x%5E2%2B2x%2B1-3%2F4-1%29;
h%28x%29=-4%28%28x%2B1%29%5E2-3%2F4-1%29
h%28x%29=-4%28%28x%2B1%29%5E2-7%2F4%29
Remultiply the -4:
highlight%28h%28x%29=-4%28x%2B1%29%5E2-7%29