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?

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I know how to find the parabola quadratic equation given the roots. However, in this problem I&#039;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&#039;d need 3 INDEPENDENT equations.So, I said, ah, I know another point, it&#039;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&#039;m left with just c=3 and 3a=4b. How, do I work this from here?

Alec Blake · Accepted Answer

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 · Accepted Answer

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  bthe 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.

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

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