Question

A parabola is graphed on a coordinate plane. The x-axis ranges from negative 2 to 10 in increments of 1. The y-axis ranges from negative 8 to 3 in increments of 1.


Identify these key features of the parabola.

Vertex: Press enter key to drop response here.Response input area

(smaller) x-intercept: Press enter key to drop response here.Response input area

(larger) x-intercept: Press enter key to drop response here.Response input area

y-intercept:

Answer 1

I can’t see the graph you’re referring to. Please either upload an image of the graph or type the coordinates of three points on the parabola (or the quadratic equation). Then I can give the exact vertex, x-intercepts (smaller = left, larger = right), and y-intercept.

If you want to find them yourself, here’s how:

- From the graph:
- Vertex = the highest or lowest point on the curve; read its (x,y) coordinates from the grid.
- x-intercepts = where the parabola crosses the x-axis (y = 0); read the x-values of those crossing points. The smaller x-intercept is the left one, the larger is the right one.
- y-intercept = where the parabola crosses the y-axis (x = 0); read that y-value.

- From the quadratic equation y = ax^2 + bx + c:
- Vertex = (h,k) where h = −b/(2a) and k = f(h) = a h^2 + b h + c.
- x-intercepts = solutions of ax^2 + bx + c = 0; use x = [−b ± sqrt(b^2 − 4ac)]/(2a). The smaller/larger correspond to the minus/plus choices if a>0 (and vice versa).
- y-intercept = c (point (0,c)).

Send the graph or equation and I’ll compute the exact values.