Question

Describe the graph of the function. y = 2x2 + 12x – 15

Answer 1

The gaph should be a parabola

Answer 2

• Interception on x-axis: (1.06, 0) and (-7.06,0)
• Axis of Symmetry, x=-3
• Minimum Point of y=-33

Explanation:

To describe the graph of the function y=
`2x^2 + 12x - 15`.

The function y=
`2x^2 + 12x - 15` is a quadratic function. All quadratic function have a parabolic curve. The direction to which the parabola opens is determined by the coefficient of
`x^2`, If the coefficient of
`x^2`, is positive as in the case above, the graph forms a downward "U" shape.

The solutions of the function y=
`2x^2 + 12x - 15` are 1.06 and -7,06, This means the graph intersects the x-axis at points 1.06 and -7.06.

To determine the axis of symmetry of a downward facing parabola,

We use the equation:
`x=-(b)/(2a)`

a=2, b=12.

Axis of Symmetry=
`-(12)/(2X2)=-3`

The minimum point is the value of y at the axis of symmetry.

`f(-3)=2(-3)^2 + 12(-3) - 15=-33`