The line y= 4x -7 is tangent to a parabola that has a y-intercept of -3 and the line x= 1/2 as its axis of symmetry. Find the equation of the parabola.

Question

anonymous · Answer

This probably isnt how you work this out.. but it's how I would have done it in highschool.

I get that the axis of symmetry is at x=.5 and so if the y was at 0 then the parabola would have zeros at x =0, x=1 so.. we can construct a parabola with those x intercepts. using +0  and -1.

(x+0)(x-1) 
Now we can reposition them on the y axis using the value -3 which gets us a parabola with the correct y-intercept
f(x)=(x)(x-1)-3
then to get the correct shape.. we stretch the parabola so that it is tangent to y=4x-7

f(x)=4x(x-1)-3

simplify
(4x*x)+(4x*-1)-3
f(x)=4x^2 -4x -3

what I can;t remember is why and how we chose 4x to get our parabola tangent to that line. There are probably a set of identities that make this really easy.. sorry it's not the best of answers

anonymous · Answer

How did you find the x-intercepts? I know you used y=0 but where did you substitute it in to find the x-intercepts?