Question

How do you find the vertex and the intercepts for `y=x^2+7x`?

Answer 1

`"see explanation"`

Explanation:

`"for intercepts"`

`• " let x = 0, in the equation for y-intercept"`

`• " let y = 0, in the equation for x-intercepts"`

`x=0toy=0larrcolor(red)"y-intercept"`

`y=0tox^2+7x=0`

`rArrx(x+7)=0`

`rArrx=0" or "x=-7larrcolor(red)"x-intercepts"`

`"the vertex lies on the axis of symmetry which is positioned"`
`"at the midpoint of the x-intercepts"`

`x_(color(red)"vertex")=(0-7)/2=-7/2`

`"substitute this value into the equation for y"`

`y_(color(red)"vertex")=(-7/2)^2+7(-7/2)=-49/4`

`rArrcolor(magenta)"vertex "=(-7/2,-49/4)`
graph{x^2+7x [-10, 10, -5, 5]}