Maths-
General
Easy

Question

Graph f(x) = -0.75x2 + 3x - 4. What are axis of symmetry, vertex and y-intercept of the function

The correct answer is: -4


                             

    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)= -0.75x2+3x-4, a= -0.75, b=3, and c= - 4. So, the equation for the axis of symmetry is given by
    x = −(3)/2(-0.75)
    x = 3/1.5
    x = 2
    The equation of the axis of symmetry for f(x)=-0.75x2+3x-4 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 = -0.75(h)2 + 3(h) - 4
    k = -0.75(2)2 + 3(2) - 4
    k = -3 + 6 - 4
    k = -1
    Therefore, the vertex is (2 , -1)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.
    y = -0.75(0)2 + 3(0) - 4
    y = 0 + 0 - 4
    y = -4
    Therefore, Axis of symmetry is x = 2
    Vertex is ( 2, -1 )
    Y- intercept is -4.

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