I know how to find the parabola quadratic equation given the roots. However, in this problem I'm giv

Frederick Kramer

Frederick Kramer

Answered question

2022-07-03

I know how to find the parabola quadratic equation given the roots. However, in this problem I'm given the y-intercept of (0,3) {So, now I know C value} and the axis of symmetry of x=-3/8. From this I know that 3a=4b. But, it seems I need one more point, since I have 3 unknowns, I'd need 3 INDEPENDENT equations.
So, I said, ah, I know another point, it's on the other side of the aos. So, I used (-3/4, 3). However, when I plug this in, it appears to not be an independent equation. So, I'm left with just c=3 and 3a=4b. How, do I work this from here?

Answer & Explanation

Alec Blake

Alec Blake

Beginner2022-07-04Added 11 answers

The point you propose to use, ( 3 / 4 , 3 ) just follows from symmetry of the parabola about x = 3 / 8. So, you are not actually fixing a degree of freedom of the parabola. In a sense, the parabola can slide up and down. Let me give 2 examples, to illustrate. Consider, y = 64 ( x 3 / 8 ) 2 / 3 which follows all the properties above, and y = 64 ( x + 3 / 8 ) 2 6 which again satisfies the properties. So, the solution to the question will not be a parabola, it will be a family of parabolas, y t ( x ) = t ( x + 3 / 8 ) 2 + 3 9 t / 64.
pablos28spainzd

pablos28spainzd

Beginner2022-07-05Added 4 answers

The symetry axis gives the point where the derivative is zero.
let y = f ( x ) = a x 2 + b x + c be the equation of the parabola.
the derivative is 2 a x + b and gives
2 a 3 8 + b = 0 or
3 a = 4 b
the point ( 0 , 3 ) satisfy the condition
3 = c.
finally, we get the expression
y = f ( x ) = a x 2 + 3 a 4 x + 3.
you have an infinite number of solutions.

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