Answer:
Vertex: (1, -4)
intercept: (-3, 0)
Step-by-step explanation:
lets be real, you don't care about an explanation you just want the answer.
BUT... the vertex is the Y line and the Intercept is the X line
The equation of a parabola is represented as [tex]\mathbf{y = a(x - h)^2 + k}[/tex]
See attachment for the graph of [tex]\mathbf{y = \frac 14(x - 1)^2 - 4}[/tex]
The given parameters are:
[tex]\mathbf{x\ intercept = -3,5}[/tex]
[tex]\mathbf{y_{min} = -4}[/tex]
Calculate the mean of the x-intercepts, to get the minimum x-value.
So, we have:
[tex]\mathbf{x_{min} = \frac{-3 + 5}{2}}[/tex]
[tex]\mathbf{x_{min} = \frac{2}{2}}[/tex]
[tex]\mathbf{x_{min} = 1}[/tex]
So, the coordinates are:
[tex]\mathbf{(x,y) = (-3,0)\ (5,0)}[/tex]
[tex]\mathbf{(h,k) = (1,-4)}[/tex] --- vertex
Recall that, the equation of a parabola is:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
Substitute [tex]\mathbf{(h,k) = (1,-4)}[/tex] and [tex]\mathbf{(x,y) = (-3,0)}[/tex] in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]
[tex]\mathbf{0 = a(-3 - 1)^2 -4}[/tex]
[tex]\mathbf{0 = 16a -4}[/tex]
Add 4 to both sides
[tex]\mathbf{16a =4}[/tex]
Divide both sides by 4
[tex]\mathbf{a =\frac 14}[/tex]
Substitute [tex]\mathbf{(h,k) = (1,-4)}[/tex] and [tex]\mathbf{a =\frac 14}[/tex] in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]
[tex]\mathbf{y = \frac 14(x - 1)^2 - 4}[/tex]
See attachment for the graph of the equation
Read more about parabolas at:
https://brainly.com/question/4074088
