Maths-
General
Easy

Question

Graph f(x) = 2x2 + 4x + 3. What are axis of symmetry, vertex and y-intercept of the function

hintHint:

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: 3


     
                                          

    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+4x+3, a=2, b=4, and c=3. So, the equation for the axis of symmetry is given by
    X = −(4)/2(2)
    x = - 4/4
    x = -1
    The equation of the axis of symmetry for f(x)=2x2+4x+3 is x = -1.
    The x coordinate of the vertex is the same:
    h = -1
    The y coordinate of the vertex is :
    k = f(h)
    k = 2(h)2 + 4(h) + 3
    k = 2(-1)2 + 4(-1) + 3
    k = 2 – 4 + 3
    k = 1
    Therefore, the vertex is (-1 , 1)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.
    y = 2(0)2 + 4(0) + 3
    y = 0 + 0 + 3
    y = 3
    Therefore, Axis of symmetry is x = -1
    Vertex is ( -1 , 1 )
    Y- intercept is 3.

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