college algebra

Question

the vertex is (10,-5) and the equation is 10x^2+bx+c how do you find b and c

Answer 1

If the vertex is (10,-5), using the vertex form the equation must be in the form y= a(x-10)² - 5

square the (x - 10) and you will have y = ax² -20ax +100a - 5 but you are given the equation is 10x² +bx+c

so, a has to be 10. This gives us y = 10x² - 200x + 1000 -5 (or 995). Thus b = 200 and c = 995.