Hi L!
Once you have the values (a, b, and c from your quadratic equation) and have plugged them into the quadratic formula, as you did above, you can use a calculator to simplify the answer.
A few notes before you proceed:
*Make sure that when you do so, you have the first (-) sign that you wrote as a (±), meaning (+) or (-). That means that there will be two solutions to the problem: one that is computed by having that symbol as addition (+), and one that is computed with that symbol as subtraction (-). This is because a quadratic equation often crosses the x-axis at 2 points, because it is U-shaped.
*The meaning of the quadratic formula, x = [-b ± sqrt(b^2 - 4ac)]/2a, is that two "solutions" (where the line passes through the x-axis, or x-intercept) are defined as (x,0) and (x,0). The quadratic formula gives you these two values for x. You find the two x values by calculating the value when the sign after (-b) is (+), and then when the sign after (-b) is (-).
*When using the calculator, just make sure to use parentheses to keep the expression consistent.
With a graphing calculator I would type: (-4.51 + √4.51^2 + 4(16)(32.81))/(2(-16)) for my first solution, and (-4.51 - √4.51^2 + 4(16)(32.81))/(2(-16)) for my second.
So, for this example, my first solution is x = -1.298 (approximately), and my solution can be written as a coordinate/x-intercept (-1.298, 0).
My second solution is x = 1.580 (approximately), and my solution can be written as a coordinate/x-intercept (1.581, 0).
This means that when graphed, the equation crosses the x-axis at these two points.
Hope this is helpful!
