How do you graph the quadratic formula x^2-10x=11? Here's what I got so far:
In standard form, it's x^2-10x-11=0.
Discriminant: -10^2-4(1)(-11)=144
Axis of Symmetry: 10^2/2(1)=50
Quadratic Formula: 56 and 44
Thank You!
<<How do you graph the quadratic formula x^2-10x=11?>>
your question makes little sense, we do not
"graph" the quadratic formula.
Are you solving the equation?
then ...
x^2 - 10x - 11 = 0
which factors nicely to
(x-11)(x+1) = 0
so x = 11 or x = -1
there is no "axis of symmetry" here, to have one you would need the corresponding quadratic function
f(x) = x^2-10x-11
You could graph this, its vertex would be (-5,64)
and the axis of symmetry for that parabola would be x = -5
To graph the quadratic equation x^2 - 10x = 11, you need to follow a few steps:
Step 1: Convert the equation to standard form: x^2 - 10x - 11 = 0. You have already done this correctly.
Step 2: Calculate the discriminant (D) using the formula D = b^2 - 4ac. In this case, a = 1, b = -10, and c = -11. Substituting these values, we get D = (-10)^2 - 4(1)(-11) = 100 + 44 = 144. Again, you have calculated this correctly.
Step 3: Determine the axis of symmetry (x = -b/2a). In this case, a = 1 and b = -10, so the equation becomes x = -(-10) / (2*1) = 10 / 2 = 5. It seems there may have been a calculation mistake on your axis of symmetry.
Step 4: Find the x-intercepts using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 1, b = -10, and c = -11. Substituting these values, we get x = (-(-10) ± √((-10)^2 - 4(1)(-11))) / (2 * 1). Simplifying further, we have x = (10 ± √(100 + 44)) / 2. This becomes x = (10 ± √144) / 2 which results in x = (10 ± 12) / 2. Therefore, the x-intercepts are x = 22/2 and x = -2/2, which simplify to x = 11 and x = -1.
Now that you have determined the axis of symmetry and the x-intercepts, you can plot the quadratic function on a graph. The axis of symmetry is a vertical line passing through x = 5. The vertex of the parabola will be on the axis of symmetry, which is at (5, f(5)).
The x-intercepts, which are the points where the parabola intersects the x-axis, are at x = 11 and x = -1.
Using this information, you can now plot the points (5, f(5)), (11, 0), and (-1, 0) on a graph. Then, you can sketch the parabolic curve that passes through these points.
Note: If you need a more precise graph, you can plot additional points or use graphing software or calculators that can graph quadratic functions for you.