Math Destroyer Test #1 Question 33
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So your equation is x^2 - 2x, and you want to find the values of x for which its y values are less than 0, aka negative.
So let's set the equation equal to 0 to find it where it's on the x-axis ---> x^2 - 2x = 0
Factoring out gives you --> x(x-2) = 0
x will equal 0 and 2 --> (0,0) and (2,0) are the points of this parabola that lie on the x-axis.
The coefficient for the x^2 term determines whether a parabola will be opening upward (positive) or downward (negative)--- (we know it's a parabola because the highest term is X^2; if it was a line, it would be just x^1 aka x).
For this equation, the coefficient is just 1 and it is positive --> the graph opens upwards in a "U" shape.
Now we know what points on it hit the x-axis, and we know its shape. Now we can determine where it will be negative (this will be below the x-axis). So, the equation is negative (aka < 0) between the values of 0 and 2, leading to C being your answer.
Here's a graphical representation. The question basically wants you to find the values of x that bound the area I shaded in yellow (as this is where the equation is less than 0 aka negative). Hope this helps! Let me know if you need any explanations on something I said. 🙂
So let's set the equation equal to 0 to find it where it's on the x-axis ---> x^2 - 2x = 0
Factoring out gives you --> x(x-2) = 0
x will equal 0 and 2 --> (0,0) and (2,0) are the points of this parabola that lie on the x-axis.
The coefficient for the x^2 term determines whether a parabola will be opening upward (positive) or downward (negative)--- (we know it's a parabola because the highest term is X^2; if it was a line, it would be just x^1 aka x).
For this equation, the coefficient is just 1 and it is positive --> the graph opens upwards in a "U" shape.
Now we know what points on it hit the x-axis, and we know its shape. Now we can determine where it will be negative (this will be below the x-axis). So, the equation is negative (aka < 0) between the values of 0 and 2, leading to C being your answer.
Here's a graphical representation. The question basically wants you to find the values of x that bound the area I shaded in yellow (as this is where the equation is less than 0 aka negative). Hope this helps! Let me know if you need any explanations on something I said. 🙂
Factor out an x and set it to 0: x(x-2) = 0. solve for x to get: x=0 and x=2.
Now pick a number less than 0 ( for example -1. -1(-1-2) = +3. Not good because we want the product to be negative ( less than 0).
Now pick a number between 0 and 2 ( 1). 1(1-2)=-1. So for the expression to be negative the value of x must be between 0 and 2.
If you pick a number greater than 2, the expression is positive. Hence the answer is : (0,2)
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