For each polynomial function, identify its graph from choices ...

Question

For each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)(x-5)

Accepted Answer

Hello, everybody. I hope we're doing all right. Today, today we're going to be looking at this map question that states consider the given polynomial function and plot its graph where our function is FX is equal to negative open parentheses, X minus 17, closed parentheses, multiplying and open parentheses, X minus 29 closed parentheses. Now when we have a function like this where we have two parentheses, multiplying each other and an X inside of those parentheses. The first thing I can think of is trying to find out the zeros or our function. So let's do that when you're trying to find the zeros. Basically, you just get whatever is inside of those parentheses and set each of them equal to zero. So we'll have one of the parentheses is X minus 17. So we'll set that equals to zero and the other parentheses was X minus 29. So we said that equals to zero. So one answer will be X is positive 17. So we move the 17 over from the left hand side to the right hand side. And for X minus 29 we move the 29 over from the left hand side to the right hand side and we'll have that X is equal to 29. So we'll have a point at 17 comma zero and another point at 29 comma zero. So next thing I'll do is solve for a Y intercept. So to do that, all we have to do is plug in 04 X. So we'll have F of zero is equal to negative open parentheses, zero minus 17, multiplying open parentheses, zero minus 29 closed parentheses. And once we distribute all that and loop up that math, we'll get an answer of negative 493 or A Y intercept of zero comma negative 493. Now, I want to once again look at my zeros and focus under multiplicity. So when we have the zero of 17 comma zero, so X equals 17 and X equals 29 have multiplicity of one, which is odd one is an odd number. Therefore, we will cross the X axis at those points. And now finally, I want to see the end of my graph. So which ways are graph points will be facing on the left and which ways are going to be facing on the right. Now, when we distribute the parentheses in our function, the X minus 17 and the X minus 29 uh we will have a value of X squared at some point and that will be the highest value of an X that we have So when we distribute those parentheses, you will have the X multiplying the X as part of that distribution, which will give you X squared. And because we have a negative outside of those fronts, we'll have negative X squared, which means graph is facing downwards on both the left and the right. So it'll be facing downward on both. And so think of it as an upside down parabola. So now that we have all that information, we can try and go ahead to make a graph of our function. So we'll draw an X axis and a Y axis and start doing some plugging in. So we will be intercepting the X axis at X equals 17 or the 170.17 comma zero. And at the point 29 comma zero, then we had a Y intercept of negative 493. So we will also have a point there and we said that both ends of our graph will be facing downwards. So from our zero at 17 comma zero to our Y intercept, we are going downwards and we continue to go downwards after that. So at negative, at a Y of negative 493 we cross the Y axis to the left. And now, and we know that from 20 the zero at 29 column zero to the right, we will also be facing downwards. And now we're just missing the connection between both our zeros. And we said we had a multiple one, which means we crossed the X axis. So we cross the X axis and we know at some point the graph is going to have to turn and head downwards like an upside down parana, which is exactly the shape of what a wrap would look like. So we have an upside down parameter with points at 17 comma zero 29 comma zero and A Y intercept of zero comma negative 400 93. So I hope that was helpful. And until next time.

For each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)(x-5)

Key Concepts

Factored Form of a Polynomial

Leading Coefficient and End Behavior

Vertex of a Quadratic Function

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