Question

I need the explanation to understand please y=x^2+10x+8A.) Identify the coefficients (a, b, and c) B.) Tell whether the graph opens up or opens down C.) Find the vertex. Write as a coordinate. D.) Find the axis of symmetry. Write as an equation. E.) Find the y-intercept Write as a coordinate.

Answer 1

We are given the equation of a parabola. Let's remember the general form for this equation:

`y=ax^2+bx+c`

The given equation is:

`y=x^2+10x+8`

Therefore, the coefficients are:

`\begin{gathered} a=1 \\ b=10 \\ c=8 \end{gathered}`

Now we will rewrite the equation to the form:

`y=(x-h)^2+k`

First we will change the equation in the following way:

`y=x^2+10x+25-17`

Now we can factor:

`y=(x+5)^2-17`

since the term (x+5)^2 is multiplied by a positive constant, this means that the parabola opens up.

The vertex of the parabola is the point (h,k), in this case, we have:

`(h,k)=(-5,-17)`

The axis of symmetry for a parabola is x = h, therefore, the axis of symmetry for this parabola is:

`x=-5`

The y-intercept is the point where x = 0, therefore, making x zero in the equation we get:

`\begin{gathered} y=(x+5)^2-17 \\ y=(0+5)^2-17 \\ y=25-17=8 \end{gathered}`

Therefore the y-intercept is y = 8.