The vertex of this parabola is at (-3, -1). When the y-value is 0, the x-value is 4. What is the coefficient of the squared term in the parabola's equation?

Question

anonymous · Answer

help me please

zale101 · Answer

Apparently, you have 2 given points
the vertex and the x-intercept
the vertex is (-3,-1)
the x-intercept is (4,0)

clear?

anonymous · Answer

no

anonymous · Answer

i dont understand any

zale101 · Answer

what part of what i just said didn't make sense to you?

anonymous · Answer

well i dont understand how to get the answer

zale101 · Answer

i know you dont understand on how to find the answer, but what about the description i made, did it make sense ?

anonymous · Answer

yes

zale101 · Answer

The equation of a parabola in a vertex form
$$y = a(x - h)^2 + k$$
vertex (h,k)=(-3,-1)
x intercept x,y=(4,0)

tat means the only variable left is a, solve for it

zale101 · Answer

Sorry about the confusion earlier, i should have used y=a(x-h)^2+k since you already mentioned it to me.

dan815 · Answer

Here is a summary of the 3 main points

dan815 · Answer

So you are given 2 points, and one of them is the vertex, at the vertex

f'(x) = 0
f ' (-3)=0  (1)
f(-3) =1   (2)
f(4)=0      (3)

So you have  these 3 pieces of information

dan815 · Answer

A parabola is a quadratic of the form y=ax^2+bx+c
you have 3 unknowns and you can form 3 linearly independent equations 

y'(-3)=0
y(-3)=1
y(4)=0

solve for a,b,c

dan815 · Answer

that 1 should be -1, fix that and carry on