How to find y-intercept using characteristics (quadratic)?

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Q: A quadratic function has these characteristics:

X= -1 in the equation of the axis of symmetry
x= 3 is the x-intercept
y= 32 is the maximum value

Determine the y-intercept of this parabola?

I thought I'd work it out like y=(x+1)[sup:2x71hwwd]2[/sup:2x71hwwd]+32

But obviously, that will give me a direction of opening not compliant with the maximum value.


I'm not very good in math so I must work on it each night. This question is the last one in my self-review so I'd like to know how to do it.

 

[Deleted member 4993]

Sorry if this is in the wrong forum, I didn't know where to put it.

Q: A quadratic function has these characteristics:

X= -1 in the equation of the axis of symmetry
x= 3 is the x-intercept
y= 32 is the maximum value

Determine the y-intercept of this parabola?

I thought I'd work it out like y=(x+1)[sup:1zw8o0a4]2[/sup:1zw8o0a4]+32 <<< Incorrect - Does it give you x-intercept = 3?

Your quadratic function looks like:

y = a * (x - 3) * (x - b)

where b is the other x- intercept.

If the curve is symetric about x = -1, where should the curve intercept x axis (given one of those is at x =3)? solve for 'b'.

Now continue to solve for 'a' - knowing the max. value of 'y'.

You can also start with:

y = a * (x+1)[sup:1zw8o0a4]2[/sup:1zw8o0a4] + 32

You can solve for 'a' - knowing one of your 'x' intercept is at x = 3