How do you graph #y= 4x^2 -24x +1#?

y = graph{ 4x^2 - 24x + 1 [-83.3, 83.3, -41.64, 41.7]}

Take a few points on either side of x = 3

x : y 6 : 1 5 : -19 4 : -31 3 : -35 2 : -31 1 : -19 0 : 1

Plot the points. Join all the points with the help of a smooth curve.

To graph the quadratic equation ( y = 4x^2 - 24x + 1 ), you can follow these steps:

1. Find the vertex using the formula ( x = -\frac{b}{2a} ).
2. Find the y-coordinate of the vertex by substituting the x-value into the equation.
3. Find the y-intercept by setting ( x = 0 ) and solving for y.
4. Find the x-intercepts by setting ( y = 0 ) and solving for x using the quadratic formula or factoring.
5. Plot the vertex, y-intercept, and x-intercepts on the coordinate plane.
6. Use the symmetry of the parabola to plot additional points on the graph if needed.
7. Draw a smooth curve passing through the plotted points to complete the graph.