Confused on a math question (1 Viewer)

[Jayjays332211]

The parabola has a turning point at (z,-8); it intersects the y-axis a y=10 and one of the x-intercepts is x=5. Find:
a) The value of z
b) The equation of the parabola

Please help :/

 

[deswa1]

Hints:
1. The general equation of a parabola is y=ax^2+bx+c
2. Sub in the two conditions for the intercepts- you'll end up with the value of c and one part of a simultaneous equation
3. Differentiate the parabola, find the value for x that makes the derivative zero and sub in the the equation, noting that the y value is -8 at this point. You'll end up with the second half of the simultaneous
4. Solve the two simultaneous equations to find a and b

 

[J-Wang]

First, find the equation. As it is a parabola, it has an x^2 and the final term is 10 as when x=0, y=10. As x=5 satisfies the equation, x^2+ax+10=0. Subbing in and rearranging gives a=-7
Therefore, the equation is x^2-7x+10

Differentiating and rearranging gives z=7/2

is that correct?

 

[deswa1]

First, find the equation. As it is a parabola, it has an x^2 and the final term is 10 as when x=0, y=10. As x=5 satisfies the equation, x^2+ax+10=0. Subbing in and rearranging gives a=-7
Therefore, the equation is x^2-7x+10

Differentiating and rearranging gives z=7/2

is that correct?

No. You assumed that the parabola was monic (the leading term was 1). This doesn't have to be the case- and isn't in the case of this question.

 

[J-Wang]

No. You assumed that the parabola was monic (the leading term was 1). This doesn't have to be the case- and isn't in the case of this question.

ahhh yes. my bad. i see how 2 do it now