Question

All you need is on the photo pleaseeeee i really need help

Answer 1

We can find the y-intercept evaluating the function for x = 0, so:

`\begin{gathered} y(x)=-5x^2+20x+60 \\ y(0)=-5(0)^2+20(0)+60=0+0+60 \\ y(0)=60 \end{gathered}`

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We can find the zeros evaluating the function for y = 0. So using the factored form:

`\begin{gathered} -5(x-6)(x+2)=0 \\ so\colon \\ x1=6 \\ and \\ x2=-2 \end{gathered}`

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The vertex V(h,k) is given by:

`\begin{gathered} h=(-b)/(2a) \\ k=y(h) \end{gathered}`

Or we can find it directly from the vertex form:

`\begin{gathered} y=a(x-h)^2+k \\ so \\ for \\ y=-5(x-2)^2+80 \\ h=2 \\ k=80 \end{gathered}`

So, the vertex is:

`(2,80)`

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The symmetry axis is located at the same point of the x-coordinate of the vertex, so the axis of symmetry is:

`x=2`

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The maximum value is located at the y-coordinate of the vertex (if it is positive) so, the maximum value is:

`y=80`