Use the parabola tool to graph the quadratic function f(x)=β5x2β2.Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Accepted Solution
A:
[tex] \text{Consider the quadratic function}\\
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f(x)=-5x^2-2\\
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\text{For a quadratic equation, }f(x)=ax^2+bx+c, \text{ we know that the x-coordinate}\\
\text{of the vertex (h,k) is given by}\\
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h=\frac{-b}{2a}\\
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\text{on comparing the given equation with standard equation, we have} [/tex][tex] a=-5, b=0, c=-2\\
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\text{so the x-coordinate of the vertex is }\\
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h=-\frac{b}{2a}=-\frac{0}{2(-5)}=0\\
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\text{so plug this vlaue of the h in the given function to get the y-coordinate}\\
\text{of the vertex. so}\\
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f(x)=-5(0)^2-2=0-2=-2\\
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\text{hence the vertex of the parabola is: }(h,k)=(0,\ -2)\\
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\text{A second point on the graph can be found by putting x=1, so }\\
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f(1)=-5(1)^2-2=-5-2=-7\\
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\text{so one other point on the parabola is }(1,-7) [/tex]The grpah of the quadratic function is shown below: