In Exercises 1–4, the graph of a quadratic function is given. Wri...

Question

In Exercises 1–4, the graph of a quadratic function is given. Write the function's equation, selecting from the following options.

Accepted Answer

Hey everyone in this problem we are asked to find out the equation of the quadratic function Using the given graph. Now we're showing the graph here And were given one point on this graph, we're told that the vertex of the graph is at -17. And if we look at the answer traces we have, we can see that these look like they're in vertex form. So let's figure this out using vertex form of a parabola. And in general the equation for a quadratic function in vertex form is going to be Y is equal to a x minus H squared plus K. Where the coordinate H. K. Is the vertex. So from this equation we can read off the vertex right away. Now in our graph we have that negative 17 is a vertex we were given and this tells us what H and K are going to be, that tells us that negative one is going to be a church and seven is going to be K. So when we write our equation we have that Y is equal to a times x minus negative one squared plus seven. And we can simplify what's in those brackets, X minus negative one is going to be X plus one squared plus set. Alright, so we have this equation to this point. What we haven't figured out is what A is yet. Now if we look at our diagram or graph we see that this parabola opens downwards. Okay. And when we have a problem that opens downwards, we expect the leading coefficient to be negative. Okay, so this tells us that we expect a to be less than zero. How can we find a? Well the things we have in our equation that aren't constant. We have Y. We have A. And we have X. So if we choose a particular point and sub in the X. And Y. Value, the only unknown will have is A. And we can solve for a. So let's choose a particular point. Now we can choose this point. We see that we have a Y intercept that occurs at 06 anytime you're plugging in a point, if you can find one of the intercepts that makes it really easy because one of those values is going to be zero. So if you can find an intercept that crosses at a you know right at a an integer value. That's going to give you a nice point. Those are the easiest points to work with. Alright so let's move and give ourselves some room to work. And again that point we found the y intercept was 06. Okay so if we substitute this into our equation we get that six. The y value is equal to a times X which is zero plus one squared plus seven. So we get that six is equal to a plus seven because we have one squared which is just one which tells us that A is equal to negative one. Okay so A is negative like we expected it's less than zero And it's equal to negative one. And so our function is going to be wise equal to negative X plus one squared plus seven. And that is the equation that represents the quadratic function in that graph. And if we look at our answer choices, we see that this matches with answer choice C. The function is going to be Y is equal to negative X plus one squared plus seven. Thanks everyone for watching. I hope this video helped see you in the next one.

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

In Exercises 1–4, the graph of a quadratic function is given. Write the function's equation, selecting from the following options.