There are five key points that can often be enough to sketch a parabolic function: the y intercept, x intercept(s), vertex, and reflection of the y-intercept across the axis of symmetry. Here we find the vertex of a parabola from letting x = -b/2a. Since "b" is zero, the x-value of the vertex will also be zero, and our axis of symmetry will be the y-axis. We find the x-intercepts here by isolating the x^2 and square rooting both sides. Alternatively, we could factor or use the quadratic formula. The y-intercept can always be found by letting x = 0 in the function, but in this case, it ends up being the same point as the vertex. Hence, we can't reflect it across the axis of symmetry, either. This is an example where our "5-point" method becomes a "3-point" method for sketching a parabola.
Transcript Coming Soon!
Please enter your name.
Are you sure you want to delete this comment?
Experience the 'A-Ha!' moment with the best teachers
whom we hand-picked for you!
M.A. in Secondary Mathematics, Stanford University B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
“Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”
“Thanks alot for such great lectures... I never found learning this easier ever before... keep up the great work.... :)”
“You seem so kind, it's awesome. Easier to learn from people who seem to be rooting for ya!' thanks”