Respuesta :
We are given the equation of a parabola. Let's remember the general form for this equation:
[tex]y=ax^2+bx+c[/tex]The given equation is:
[tex]y=x^2+10x+8[/tex]Therefore, the coefficients are:
[tex]\begin{gathered} a=1 \\ b=10 \\ c=8 \end{gathered}[/tex]Now we will rewrite the equation to the form:
[tex]y=(x-h)^2+k[/tex]First we will change the equation in the following way:
[tex]y=x^2+10x+25-17[/tex]Now we can factor:
[tex]y=(x+5)^2-17[/tex]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:
[tex](h,k)=(-5,-17)[/tex]The axis of symmetry for a parabola is x = h, therefore, the axis of symmetry for this parabola is:
[tex]x=-5[/tex]The y-intercept is the point where x = 0, therefore, making x zero in the equation we get:
[tex]\begin{gathered} y=(x+5)^2-17 \\ y=(0+5)^2-17 \\ y=25-17=8 \end{gathered}[/tex]Therefore the y-intercept is y = 8.
