Question Video: Simplifying Rational Functions Using Factorization Then Finding Their Zeros | Nagwa Question Video: Simplifying Rational Functions Using Factorization Then Finding Their Zeros | Nagwa

# Question Video: Simplifying Rational Functions Using Factorization Then Finding Their Zeros Mathematics • Third Year of Preparatory School

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Write the quadratic equation represented by the graph shown.

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### Video Transcript

Write the quadratic equation represented by the graph shown.

We begin by observing the general shape of the given graph. It is a parabola, meaning that it is the graph of a quadratic function and it has a line of symmetry given by the π¦-axis or the equation π₯ equals zero. This means its equation will be of the form π of π₯ equals π times π₯ squared plus π, with π not equal to zero.

Our job now will be to identify the values of π and π. We recall that the π¦-intercept of the function is found by calculating π of zero. For an equation of the form π of π₯ equals π times π₯ squared plus π, we find that π of zero equals π. The quadratic graph shown has a π¦-intercept of two. Thus, π equals two. This allows us to write our equation as π of π₯ equals π times π₯ squared plus two.

Next, we can calculate the value of π by choosing any point that lies on the given parabola. Letβs choose two, negative two. This tells us that π of two equals negative two. We will proceed by substituting two for π₯ in our equation. By simplifying, we show that π of two equals four π plus two. To solve for π, we will use the fact that π of two also equals negative two from the graph. This gives us the equation negative two equals four π plus two. To solve this equation, we subtract two from each side of the equation. Then, we divide by four. The result is π equals negative one. In fact, we would expect π to be less than zero since the parabola opens down, or is n shaped.

Now that we know that π equals two and π equals negative one, we can write the equation for the given quadratic graph. The quadratic equation represented by the graph shown is π of π₯ equals negative π₯ squared plus two.

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