SOLUTION: Find vertex and y-intercept of the equation y=0.5x^2+6x+10

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find vertex and y-intercept of the equation y=0.5x^2+6x+10      Log On


   

Question 254298: Find vertex and y-intercept of the equation y=0.5x^2+6x+10
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
here is the equation:
y=0.5x%5E2%2B6x%2B10
step 1 - factor .5 out of the first two terms like this:
y=0.5%28x%5E2%2B12x%2B+_____%29+%2B+10+-+______
The blanks are waiting for numbers as you complete the square.
step 2 - take 1/2 of the middle term and put that answer in the first blank. LIke this:
y=0.5%28x%5E2%2B12x%2B+6%5E2%29+%2B+10+-+______
step 3 - multiply 36 by 1/2 to get 18. put this in the second blank. Notice the sign.
y=0.5%28x%5E2%2B12x%2B+6%5E2%29+%2B+10+-+18
step 4 - rewrite the first (_) as a quantity squared and simplify that last 2 numbers as
y=0.5%28x%2B6%29%5E2+-+8
This is in vertex form.
The vertex is (-6, -8)
Y-intercept is when x = 0.
(0,10)