How do you identify the important parts of #y= -7x^2 +2x# to graph it?

Question

Avery Alexander · Accepted Answer

The given equation represents a parabola.

On simplifying the equation,we get -(y-1/7) = (#sqrt7#x -1/#sqrt7# )^2 This equation represents a parabola with vertex (1/7,1/7) graph{-7x^2+2x [-0.377, 0.8064, -0.33, 0.2623]}

Eva Abramson · Answer

undefined To graph the function $ y = -7x^2 + 2x $, follow these steps to identify the important parts:

1. **Vertex:** Use the formula $ x = -\frac{b}{2a} $ to find the x-coordinate of the vertex. Then, substitute this value into the equation to find the corresponding y-coordinate.
2. **Axis of Symmetry:** The axis of symmetry is the vertical line that passes through the vertex. Its equation is $ x = \frac{-b}{2a} $.
3. **Y-intercept:** Substitute $ x = 0 $ into the equation to find the y-intercept.
4. **X-intercepts (if any):** Set $ y = 0 $ and solve the quadratic equation $ -7x^2 + 2x = 0 $ to find the x-intercepts.
5. **Direction of Opening:** Since the coefficient of $ x^2 $ is negative, the parabola opens downwards.

Once you have this information, you can plot the points and sketch the graph of the quadratic function.