SOLUTION: Write and equation in standard form, factores form, and vertex form for a parabola with a vertex of (6,-15.2) x-intercepts: (2,0) and (10,0)

Algebra ->  Linear-equations -> SOLUTION: Write and equation in standard form, factores form, and vertex form for a parabola with a vertex of (6,-15.2) x-intercepts: (2,0) and (10,0)      Log On


   

Question 1001381: Write and equation in standard form, factores form, and vertex form for a parabola with a vertex of (6,-15.2)
x-intercepts: (2,0) and (10,0)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Make a plan for what to do. One possible plan could be this:

(1) Use factored form according to the x-intercepts but keep the constant factor, "a", as variable.
(2) Solve the equation for the factor "a", and substitute the vertex coordinates to find the value of "a".
(3) Express the completed equation in factored form.
(4) Write in standard form according to the known vertex (already given) and now known factor, "a". Understand, STANDARD FORM is the same as VERTEX FORM.


You could instead simply do this, for a different plan:
y=a%28x-6%29%5E2-15.2
and then
a=%28y%2B15.2%29%2F%28x-6%29%5E2
use either of the x-intercepts
a=15.2%2F%2810-6%29%5E2
a=15.2%2F16
a=0.95
and you have the standard form equation as y=%280.95%29%28x-6%29%5E2-15.2. Getting factored form from this may be more difficult than using the plan described first, above.