Question

How do you graph the function, label the vertex, axis of symmetry, and x-intercepts. y=−3x2−12x−3?

Answer 1

Given:

y=−3x²− 12x − 3

To Find:

The vertex, axis of symmetry, and x-intercepts.

Solution:

• Vertex is the point where the tangent to the parabola is parallel to x axis.
• Axis of symmetry is the axis passing through the vertex cutting the parabola equally.
• X intercepts are the roots of the parabolic function.

   1. To find vertex ,

• Take dy/dx = 0
• 6x - 12 = 0
• x = 2
• y = 3x2² - 12x2 - 3 = 12 - 24 - 3  = -15
• Vertex is ( 2 , -15 )

    2.  To find axis of symmetry,

• Since this is a standard parabola , vertex will be perpendicular to the x axis.
• Vertex will be parallel to y axis.
• Its a line where x  =  a constant
• Here x = x coordinate of vertex .
• x  = 2 , is the axis of symmetry.

    3. To find the x intercepts,

• Let y = 0 .
• This gives that values of x for which the parabola meets the x axis.
• 0 = 3x² - 12x - 3
• x² - 4x - 1 = 0
• x = 4 ± √16 +4 / 2
• x = 2 ± √5
• Therefore the x intercepts are 2+√5 and 2-√5 .

( 2 , -15 )  is the Vertex , x  = 2  is the axis of symmetry and 2+√5 and 2-√5  are the x intercepts of the function, y = 3x² -12x -3.