# Quadratic function problem.?

find the rule of correspondence for a quadratic function whose graph has the indicated features. Write the rule in standard form.

1. x- intercepts at (-3,0) and (1,0); the same shape as y=x^2

2.x- intercepts at (7/2,0) and (5,0); the same shape as y= -3x^2

what do you mean this is straight out of the textbook the question, I'm trying to figure out how you don't understand what rule of correspondence means.

### 1 Answer

- Ray SLv 79 years agoFavorite Answer
➊ For y = ax² + bx + c

If h and k are zeros of the quadratic function, then (x-h) and (x-k)

are factors of it ... zeros being the value(s) of x that make

the function zero, i.e. the value(s) of x that produce y=0.

Notice that this doesn't allow for all coefficients 'a' of x²:

➋ y = (x-h)(x-k) = x² -hx - kx + hk = x² + (-h-k)x + hk ← b = (-h-k)

c = hk

But, 'a' can only be 1.

So, we need to incorporate 'a' into ➋.

That modifies ➋ to the final form

➌ y = a(x-h)(x-k)

Now, using ➌, your problems become easy to do.

——————————————————————————————————————

1. x-intercepts at (-3,0) and (1,0); the same shape as y = x².

Note:

x-intercepts are the zeros of the function ... i.e. 1 & -3 are zeros

and the same shape as y = x² indicate that a=1.

So,

➌ y = a(x-h)(x-k) = 1(x-1)(x-(-3)) = (x-1)(x+3) = x²+2x-3

y = x²+2x-3 ← ANSWER

——————————————————————————————————————

2. x-intercepts at (7/2,0) and (5,0); the same shape as y= -3x²

Note

x-intercepts are ⁷∕₂ & 5 and a = -3

So,

➌ y = a(x-h)(x-k) = -3(x-⁷∕₂)(x-5) = (x-⁷∕₂)(x-5) = -3x²+(⁵¹∕₂)x - ¹⁰⁵∕₂

y = -3x²+(⁵¹∕₂)x - ¹⁰⁵∕₂ ← ANSWER

Hope this is what you are looking for.

Have a good one!

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