We are asked to find an equation with roots at - 6 and 15. We can investigate the axis of symmetry of the quadratic functions to find the correct answer. We can find the axis of symmetry two ways. The first is by using the roots. The roots are symmetric to the axis of symmetry, so we can use the given roots to find it.
Average of Roots:& -6+ 15/2=-2.9
Axis of Symmetry:& x=-2.9The second method is using the coefficients of the quadratic to find the axis of symmetry.
Quadratic Function:& f(x)= ax^2+ bx+ c
Axis of Symmetry:& x=-b/2 a
Let's find the axis of symmetry for all options.
Option
Equation
Axis of Symmetry
Expression
Equation
A
y= 5x^2 -29x -6
--29/2( 5)
x=2.9
B
y= 5x^2+ 31x+ 6
-31/2( 5)
x=-3.1
C
y= 5x^2+ 29x -6
-29/2( 5)
x=-2.9
D
y= 5x^2 -31x+ 6
--31/2( 5)
x=3.1
We can see that only one axis of symmetry matches the one we found using the roots. The correct answer is C.
