year 11 extended response past exam question help?

[TMJ]

This question has just confused me so help would be excellent.

 A quadratic function is defined by f: [-5,2] ----> R and the rule f(x)=ax^2+bx+c. The turning point has coordinates (-2,9). The minimum value of the function is -7. Find the values of a, b, and c.

[b^3]

If you write it in turning point form, that is in the form , you can find the values of and from the turning point given. Then you can do a little sketch of the graph. Since we are told the minimum is -7 and the y value of the turning point is 9, we know that our turning point cannot be a minimum, and so has to be a maximum. That is we have an inverted parabola. So you can do the little sketch, but notice that the domain for . Now we can notice that the end of the domain that is furthest away from out turning point is , so at the value will be our minimum, . So now you have a point and one unknown, with the equation , so you can solve for . What you will end up with is the equation in turning point form, so you need to expand it out, then you will get the values of , and .

Hope that helps

EDIT: Fixed the error.

Have a try before you check this :)