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The function f(x)f(x) is a quadratic function and the zeros of f(x)f(x) are 11 and 55. The y-intercept of f(x)f(x) is 2020. Write the equation of the quadratic polynomial in standard form.

Sagot :

JeanaShupp

Answer: [tex]4x^2 -24x+20[/tex]

Step-by-step explanation:

If p and q are zeroes of f(x), then f(x) = k (x-p)(x-q) , where k is a constant.

Given: The function f(x)f(x) is a quadratic function and the zeros of f(x)f(x) are 1 and 5.

f(x) = k (x-1)(x-5)

y-intercept = Value of function at x=0

So, y-intercept =  k (0-1)(0-5)= 5k

Since,  y-intercept of f(x) = 20

so, 5k = 20

⇒ k= 4

Quadratic polynomial [tex]= 4(x-1)(x-5)[/tex]

[tex]=4(x^2-6x+5)\\\\= 4x^2 -24x+20[/tex]

Hence, the equation of the quadratic polynomial in standard form =[tex]4x^2 -24x+20[/tex]

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