Find b and c so that y = 14 x 2 + b x + c has vertex ( 3 , 6 ) .

Question

Help, please.

Answer 1

Just a WAG Wild A Guess, but b=-84, c=132

a=14

V(3,6) in a standard parabola quadratic means

y= a(x-3)^2 + 6

expand and look for the coefficients of the x^2 term, x term and the constant term

Answer 2

Traditionally, we are given an equation and asked to find a vertex, in this problem, the reverse scenario is given.

To find the x-value of the vertex of an equation, we use the formula x = -b / 2a where the equation of a quadratic formula is y=ax²+bx+c.

This would yield 3 = -b/ 2(14) solving this equation would go as follows...

3 = -b/28

84 = -b

b = -84

To find c, simply plug your value for b, x, and y into your equation and solve for c

y = 14x²-84x+c

6 = 14(3)²-84(3) +c

6 = 14(9)-249+c

6 = 126 - 249 +c

6 = -123+c

129 =c