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Determine the zeros and then, using the sign of the function, draw its sketch.$$f(x)=x^{2}-x-12$$

$$-3,4$$

Algebra

Chapter 1

Functions and their Applications

Section 7

More on Functions

Functions

Campbell University

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University of Michigan - Ann Arbor

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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Determine the zeros and th…

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Find the zeros (if any) of…

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(a) determine the real zer…

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Find the zeros of the func…

to determine the zero of this function. We can factor this function like this. And then it's easy for us to see that the solutions, uh X equals minus three and X equals four. And to draw the graph of this function, I used a programming language pistol. And here is a graph, as we can see when X is smaller than minus three and when X is greater than four. This function is positive and one access between man or three and for this function is negative and therefore it has choose solutions. X equals minus three and X equals four here. I also want to mention the quadratic formula, so when you can't factor the function easily, you can use this formula this for Marseille's when the function has a quadratic form here a, B and C r. All coefficient and ex easy and no. So we discussed the solution into three situations in situation. One be square miners. Four time, they say, is greater than zero. Then this quadratic function has two solutions which are X one and X two in situation to one be square manners Four times they say equals zero. This quadratic function only has one solution, which is miners be over to a in sexual 18 31 B Square miners four times they say, is smaller than zero. This quadratic equation has no solutions. I want to emphasize here that in all these three situations, the solution formula is consistent. As you can say in situation to when B squared times for is equal zero, this term disappears and the solution x one becomes a solution X and in situations three When B squared times for a say is smaller than zero, this term is not a real number. Enhance. It has no real solutions. And now let's verify this formula. Exercise one. So in exercise one A equals one B equals minus one and say equals minus 12. So use this formula. We have X y equals ministry and X two equals four, which is the same as the above solution

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