Question

Check my work?

The question: What are the solutions of 3=4x^2 -4x?
I entered y=4x^2 -4x+3 into a graphing calculator and my answer is there are no x-intercepts so there are no solutions.

Is this correct?

Answer 1

Incorrect.

If you wanted to solve this graphically, you would need to enter 4x^2 -4x - 3 and determine the zeros.

Answer 2

Or you can enter Y1 = 3
Y2 = 4x^2 - 4x

and see where they intersect.

If the dont intersect, then you'll know there is no solution.

Answer 3

3=4x^2 -4x

you needed to subtract 3 on both sides... you added 3 on both sides

Answer 4

Okay, that makes sense. Thank you to both of you! One more question: When I graph 4x^2-4x-3, it is a parabola so how do I know if there are any solutions? Easyaspi said if it doesn't intersect then you know there isn't any solutions so does that mean that parabola never have solutions?

Answer 5

@Easyaspi314 @agent

Answer 6

@agent0smith

Answer 7

If you graph 4x^2 -4x - 3....you are looking if that graph (of the parabola) intersects the x-axis. If it intersects the x-axis, then it has solution(s). Otherwise, there is no solution.

Answer 8

If it touches the x axis, it has real solutions

You can also use the discriminant, b^2 - 4ac to decide if it has solutions.

Answer 9

Ohh, okay. Now I get it. Thank you guys sooo much! I understand it now. Thanks!

Answer 10

welcome.