Maths-
General
Easy

Question

Find the axis of symmetry, vertex and y-intercept of the function
f(x) = 2x2 + 8x + 2

Hint:

For a quadratic function is in standard form, f(x)=ax2+bx+c.
A vertical line passing through the vertex is called the axis of symmetry for the parabola.
Axis of symmetry x=−b/2a
Vertex The vertex of the parabola is located at a pair of coordinates which we will call (h, k). where h is value of x in axis of symmetry formula and k is f(h).
The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.
 

The correct answer is: 2


    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= 2x2 + 8x + 2, a= 2, b= 8, and c= 2. So, the equation for the axis of symmetry is given by

    x = −(8)/2(2)

    x = -8/4

    x = -2
    The equation of the axis of symmetry for f(x)= 2x2 + 8x + 2 is x = -2.
    The x coordinate of the vertex is the same:

    h = -2
    The y coordinate of the vertex is :

    k = f(h)

    k = 2(h)2 + 8(h) + 2

    k = 2(-2)2 + 8(-2) + 2

    k = 8 – 16 + 2

    k = -6
    Therefore, the vertex is (-2 , -6)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = 2(0)2 + 8(0) + 2

    y = 0 + 0 + 2

    y = 2
    Therefore, Axis of symmetry is x = -2
    Vertex is ( -2 , -6)
    Y- intercept is 2.

    Related Questions to study

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.