Answer:
Therefore, the standard for will be:
[tex]y=\frac{1}{4}x^{2}-x-4[/tex]
Step-by-step explanation:
The equation of a parabola written as vertical axes is given by:
[tex](x-h)^{2}=4p(y-k)[/tex] (1)
The vertex of the parabola (h,k) is (2,-5).
The focus (h,k+p) is (2,-4)
Then we can find p knowing that:
h = 2
k = -5
k + p = -4 then p = -4+5 = 1
Putting all these values in equation (1) we will find the equation of the parabola:
[tex](x-2)^{2}=4(1)(y-(-5))[/tex]
[tex](x-2)^{2}=4(y+5)[/tex] (2)
Now, we need to find the standard form of the equation of the parabola.
Let's recall that standard form is:
[tex]y=ax^{2}+bx+c[/tex]
We just need to work out equation (2) to convert it to the standard form.
[tex](x-2)^{2}=4(y+5)[/tex]
[tex]x^{2}-4x+4=4(y+5)[/tex]
[tex]\frac{1}{4}x^{2}-x+1=y+5[/tex]
Therefore, the standard for will be:
[tex]y=\frac{1}{4}x^{2}-x-4[/tex]
I hope it helps you!
