Question

How do you find the vertex and the intercepts for `y - 10 = 15 + x^2 + 2x`?

Answer 1

minimum at `(-1,24)` and y-intercept is `25`

Explanation:

`y-10 = 15+x^2+2x`

rearrange,
`y = x^2+2x+25`

y - intercept, when x=0,
`y = 25`

there is no x-intercept since `b^2-4ac < 0` where `a=1, b=2 and c=25`

by completing a square,
`y=(x+1)^2-(1)^2+25`
`y=(x+1)^2+24`
This is a minimum vertex because there is a +ve coefficient for `(x+1)^2`

therefore, it vertex is minimum at `(-1,24)` and y-intercept is `25`