In Exercises 17–38, use the vertex and intercepts to sketch the g...

Question

In Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=4−(x−1)^2

Accepted Answer

Drive the graph of the given quadratic equation Using vertex and intercepts. Also find the domain and range. Using a graph and find the equation of the axis of symmetry. My equation is 13 minus parentheses. three X -6 sq. Let's first find the vertex to find that I'm going to factor out that three x minus six squared 13 -3 x -6 times three x -6. You go ahead and foil this. We get nine X squared minus 18 x minus 18 X plus 36 13 -9 x squared plus 36 X minus 36. Simplifying even further we get negative nine X squared Plus x minus 23. To find our vertex we will take X equals negative B over two A. We're in a quadratic, we have X squared plus bx plus C. So our vertex we find our X. X will be. Now you have 36/2 times negative nine. Now get 36/18 negative which is equal to to the x component of Vertex is too Let's find the wagon opponent. The black opponent. Well, let me plug in our two into the equation 13 -3 times 2 -6 squared. You notice here we get 6 -6 inside which goes to zero. This one's out to be 13. So our vertex is 2 13. This also means our acts of symmetry Will be X is equal to two. It's X equals to the X component of our vertex. Now we need to find what our intercept. Sir. Let's go ahead and find our our x intercepts. So we can say zero is equal to 13 minus three x minus six square. We want to solve for x two pac 13. 1st get negative, 13 is equal to negative three x minus six squared divide by negative one. To get 13 equals three x minus six square. Now we'll take the square root of both sets. So we get squared of 13 plus or minus. It's equal 23 X -6. Let's go ahead and simplify this a little bit more. Add 6 to both sides. We get six posted miles squared of 13 is equal to three X. Finally divide everything by three to get X is equal to six plus or minus square of 13 over three. So now we have two points. We can use Our intercepts were to plug this in the calculator, get x equals 0.798 and X is equal to 3.202. Going to find which one of these answers corresponds to all of our information that we have. We have vertex to 13 points As 0.798 zero And 3.2020. So if you look here the first one domain name, infinity to infinity range negative infinity to 13. Axis of symmetry is X is equal to two. We know axis symmetry is equal to the two. Our domain should be all real numbers And finally our range, it should have 13 as the highest possible value. That means the answer to our problem. It's going to be equal to answer A Which is this graph right here. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=4−(x−1)^2

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