How do you use the important points to sketch the graph of #F(x)=3x^2+4x-1 #?

Question

Nathan Axel · Accepted Answer

As an example of method look at https://tutor.hix.ai

Ethan Adkins · Answer

undefined To sketch the graph of $ F(x) = 3x^2 + 4x - 1 $, you can follow these steps:

1. Determine the vertex of the parabola using the formula $ x = -\frac{b}{2a} $.
2. Find the y-coordinate of the vertex by substituting the x-coordinate into the function.
3. Locate the y-intercept by setting $ x = 0 $ and solving for $ y $.
4. Find the x-intercepts by solving the quadratic equation $ 3x^2 + 4x - 1 = 0 $.
5. Plot these points on a coordinate plane.
6. Determine the direction of the parabola by examining the coefficient of $ x^2 $ (positive coefficient means the parabola opens upwards, negative coefficient means it opens downwards).
7. Sketch the parabola passing through the plotted points, making sure it is symmetric around the axis of symmetry.

These steps will help you sketch the graph of the given quadratic function.