# How do you graph 7x^2+5x+10?

Aug 2, 2015

Graph y = 7x^2 + 5x + 10

#### Explanation:

To graph a quadratic function, find some critical points of the parabola.
If a > o, the parabola opens upward.
Find the vertex and axis of symmetry.
x-coordinate of vertex, and axis of symmetry: x = (-b/(2a) = -5/14
y-coordinate of vertex: f(-5/14) = 375/196 = 1635/196 = 8.34
y-intercept -> x = 0 --> y = 10.
x-intercepts -> Solve y = 7x^2 + 5x + 10 = 0
D = 25 - 280 = -255 < 0. There are no x-intercepts. The parabola is completely above the x-axis.
graph{7x^2 + 5x + 10 [-40, 40, -20, 20]}