Thread: This parabola question baffles me!

A very good day to everyone here.

I would like you to help me solve this question:

What I don't understand:
Candidly, I don't know how to do this whole question. All I know is that the quadratic formula is . But how can this formula be applied in finding ?

You know point A is (0,8)

Substitute x = 0, y = 8, into the equation of the graph, y = (x+p)(2-x) and solve for p. Once you have p, you can solve the rest.

Hello Educated, here's my working for (a)









What are the coordinates of point B?
The question doesn't state any value for x nor y. It's so tough.

Now that you have the equation, do you know how to find the roots of an equation? To make y = 0?



If x = 2, y = 0. This one is given for you, it's point c.
If x = ..., y = 0. This one you can solve yourself.

Solve the second root and that's the x-coordinates for b.

Oh, I see, so I'll take as , hence-


or

or

Now, since the value must be negative at the point ,
I should reject and take as the answer.

Also, the value at point must be .

Hence B is (-4,0).

Now I would have to do part (c).

The line of symmetry is the midpoint of the parabola.

What am I suppose to do now?

Midpoint of the parabola is halfway between the 2 roots.

So is the line of symmetry equals to :



?

Yep. Remember that it's only the vertical line that can make it symmetrical.

Thank you so much for your help, Educated! My problem is finally solved.