I did the math for the previous problem I posted, using this formula: -b+ or - the square root of b^2-4ac/2a. When I did this for -x^2+2x-1, I got 0/-2. I did the math and the x and y intercept came out to be -2 and -2. But when I graphed this on my graphic calculator, the points didn't cross through -2, and my answer sounds wrong. How can I fix this?
a=-1 b=2 c=-1
b^2-4ac is zero
x=-1, double root. I don't know how you got zero and -2
by using the formula you should get
x1=x2=1
so your graph will be upside down porabola with y intercept at -1 so the graph will cut the y-axis at -1, and touch the x-axis at 1.
:)
Thank you no name. :)
To solve quadratic equations using the quadratic formula, which is -b±√(b^2-4ac)/2a, it's important to follow the correct order of operations. Let's break down the steps to help you find the correct solution:
1. Start with the equation: -x^2 + 2x - 1 = 0. Identify the values of a, b, and c.
- In this case, a = -1, b = 2, and c = -1.
2. Plug these values into the quadratic formula:
- x = (-b±√(b^2-4ac))/(2a)
- x = (-(2)±√((2)^2-4(-1)(-1)))/(2(-1))
- Simplifying further:
x = (-2±√(4-4))/(-2)
x = (-2±√0)/(-2)
x = (-2±0)/(-2)
x = -2/(-2)
x = 1
So, the solution to the equation -x^2 + 2x - 1 = 0 is x = 1.
It's important to note that you obtained -2 as an answer because you mistakenly performed the operations incorrectly. This highlights the importance of cautiously following the order of operations.
When graphing the equation y = -x^2 + 2x - 1, you should indeed see the point (1, 0) as the x-intercept (where the graph crosses the x-axis) since x = 1 is the solution. However, there may be no y-intercept (where the graph crosses the y-axis) at -2, as you initially expected. The y-intercept can be determined by substituting x = 0 into the equation, giving y = -1. Therefore, the y-intercept is (0, -1).
To confirm the solution graphically, make sure you entered the equation correctly in your graphic calculator. Double-check the signs and the order of terms.