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+3x−10

Accepted Answer

Graph the parabola defined by F of x equals x squared minus four x minus five by using its vertex and intercepts determine the equation of axis of symmetry and identify domain and range based on the graph. Let's find our vertex first. Our vertex we can use the equation X equals negative B over two A. This will help us find the X component of the vertex we know quadratic is given by X squared plus bx plus C. So we can look at our equation. This means our B turned out to be negative four. So Top we have -94. Bottom too. Our X is one. Our sorry, a is one. So we get 4/2 which is equal to two. Now you can take that and plug it back in to find what our way is for the vertex F of two is equal to two squared minus four times two minus five. Just four minus eight minus five. This simplifies out to be or minus eight, negative four minus five, negative nine. So our vertex happens at two negative nine. Now we can find our intersects. Why intercept? Well x equal to zero zero is equal to zero squared minus four times zero minus 54. Now you're the five. So are white intercept happens at the 0 -5. But so you can find the graph that has vertex to negative nine. Y intercept zero negative five. We noticed you can't be graphic because it has the wrong vertex, graph B looks like we have the craigs vertex. And the crowds Y intercept. Let's check. C C has the incorrect vertex and graph D also has the incorrect vertex. So looking at graph B, our axes of symmetry will be given by X equals the X coordinate of the vertex X equals two. Based on this graph, we can tell our domain is from negative infinity to infinity. Our range starts at negative nine at the bottom goes up all the way to infinity. The answer to our problem then turns out to be answer B. Okay. I have 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+3x−10

Watch next

Quadratic Functions practice set