determine the values of a and b in the relation ax^2+bx-6 if the vertex of the graph is at (-2,6)

Answer 1

Hi Maryanne, using the formula for the axis of symmetry, x = -b / 2a, we can find a value of b as it relates to a.

x = -b / 2a

Replace x by -2, from the vertex:

-2 = -b / 2a

Solve for b:

-b = -4a

Or

b = 4a

The y-value from the vertex is found by evaluating equation using the x-value of the vertex:

y = ax² + 4ax - 6

Substitute 6 for y, and -2 for x:

6 = a(-2)² + 4a(-2) - 6

6 = 4a - 8a - 6

solve for a:

a = -3

Substitute for a in the equation, b = 4a, b = -12

The value for a is -3.

The value for b is -12

Questions?