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I need help on my algebra project i have part A completed.

I need help on my algebra project i have part A completed.-example-1

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Solution

Given the function below


f(x)=(x-a)(x-b)

To create a new parabola in the pattern of the parabola above,

Let


a=1\text{ and b}=1

Thus, the above function becomes


f(x)=(x-1)(x-1)

Opening the brackets gives


\begin{gathered} f(x)=x(x-1)-1(x-1) \\ f(x)=x^2-x-x+1 \\ f(x)=x^2-2x+1 \end{gathered}

The leading coefficient is greater than 0 i.e


x^2\text{ has a leading coefficient of 1 and it is greater than 0}

Since the leading coefficient is greater than 0, the parabola opens upwards.

Hence, the direction of the parabola is upwards.

The zeros of the f(x) will be


\begin{gathered} x-1=0 \\ x=1 \\ x-1=0 \\ x=1\text{ (twice)} \end{gathered}

The zeros of the polymial is 1 (twice)

The graph of the created function is

From the graph above,

The y-intercept of the function is 1

I need help on my algebra project i have part A completed.-example-1
User Tomasz Lewowski
by
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