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General
Easy

Question

Identify the y – intercept , axis of symmetry , and vertex of the graph of each function . H(x)= -3x2+7x+1

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: ( 1.167 , 5.083 )


    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 H(x)= -3x2+7x+1, a= -3, b=7, and c=1. So, the equation for the axis of symmetry is given by
    x = −(7)/2(-3)
    x = - 7/-6
    x = 7/6
    The equation of the axis of symmetry for H(x)= -3x2+7x+1 is x = 7/6.
    The x coordinate of the vertex is the same:
    h = 7/6
    The y coordinate of the vertex is :
    k = H(h)
    k = -3(h)2 + 7(h) + 1
    k = -3(7/6)2 + 7(7/6) + 1
    k = -(49/12) + (49/6) + 1
    k = 5.083
    Therefore, the vertex is (1.167 , 5.083)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.
    y = -3(0)2 + 7(0) + 1
    y = 0 + 0 + 1
    y = 1
    Therefore, Axis of symmetry is x = 7/6
    Vertex is ( 1.167 , 5.083 )
    Y- intercept is 1.

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