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)=x^2+6x+3

Accepted Answer

Graph the parable defined by f of x X squared minus six. X plus five. By using its vertex and intercepts determine the equation of access to symmetry. Can identify the domain remains based on the graph. Let's find our vertex. First vertex we can find using negative B over two A. Is equal to X or R X component. Question of problem is given by X squared plus bx plus C. Our equation can say X equals R. B. Which is negative six Over two times a. Which is just one. We get 6/2, which is equal to three. The X component will be equal to three. Now let's go ahead and find the white component. So why is there f. f 3? Which is gonna be three squared minus six times three plus five. It's nine -18 Plus five. That turns out to be -4. So our vertex happens at 3 -4. Let's find their intercepts. Our x intercept were given by Y is equal to zero. So let's say zero equals x squared minus six. X plus five. Now this is a factor, we can factor this as X -1, X -5. Software X we get x minus one equals zero, X minus five equals zero or X equals one at x equals five. We then have two, X intercepts At 1, 0 and 50. You can also find our wider sense By Letting X is equal to zero. So I say y is equal to zero squared minus six times zero plus five, or y is equal to five. We then have a Y intercept at 05. Let's find the graph that has all of these points texas 3 4 intercepts 1050. And why intercept 05 that looks like it matches with graphic a. Our extra symmetry then will be X is equal to the X coordinate of the vertex X equals three. We can see our domain is an equal tonight, infinity to infinity. Our range starts at negative four at the bottom goes up to infinity. That means the answer to our problem turns out to be answer. A. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

Struggling with College Algebra?

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)=x^2+6x+3

Watch next

Quadratic Functions practice set