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Explain how to determine the quadratic equation using linear factors and zeros of the graph below.

Explain How To Determine The Quadratic Equation Using Linear Factors And Zeros Of The Graph Below class=

Sagot :

Answer:

[tex]f(x)=-x^2+11x-28[/tex]

Step-by-step explanation:

We see that the zeroes of the graphed parabola are [tex]x=4[/tex] and [tex]x=7[/tex], which are solutions to [tex]x-4=0[/tex] and [tex]x-7=0[/tex] respectively. We also observe that the parabola opens downward, so the leading coefficient is negative. By multiplying these two factors and negating the result, we can determine the actual function:

[tex]f(x)=-(x-4)(x-7)\\\\f(x)=-(x^2-11x+28)\\\\f(x)=-x^2+11x-28[/tex]

Thus, the quadratic equation represented by the graph is [tex]f(x)=-x^2+11x-28[/tex]

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