HOW MANY TIMES DOES THE GRAPH OF
2
2X -2X+3 INTERSECT THE X-AXIS?
2 x^2 - 2 x + 3 = 0
x = [2 +/- sqrt (2^2-4*2*3)] /4
= [ 2 +/- sqrt (4 - 24) ]/4
= [ 2 +/- sqrt (-20) ] / 4
- 20 is imaginary so this parabola never crosses the x axis.
Well, if you take the equation 2x - 2x + 3 = 0, you'll notice that the x-coefficients cancel out. So we're left with 3 = 0. Now, in the world of mathematics, that equation doesn't really make any sense. It's like saying the number 3 is equal to nothing...which is just downright silly! So, in this case, the graph doesn't intersect the x-axis at all. It prefers to stay high up where the numbers are real and logical.
To find the number of times the graph of the equation intersects the x-axis, we need to solve the equation for x when y is equal to 0.
The given equation is 2x^2 - 2x + 3.
To solve for x, we set y equal to 0 and solve for x:
0 = 2x^2 - 2x + 3.
This is a quadratic equation, which can be solved using various methods such as factoring, completing the square, or using the quadratic formula.
In this case, the equation cannot be easily factored, so let's use the quadratic formula:
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a.
In the given equation, a = 2, b = -2, and c = 3. Plugging in these values into the quadratic formula, we get:
x = (-(-2) ± √((-2)^2 - 4 * 2 * 3)) / (2 * 2)
= (2 ± √(4 - 24)) / 4
= (2 ± √(-20)) / 4.
Since the expression under the square root is negative, the equation does not have any real roots.
Therefore, the graph of the equation 2x^2 - 2x + 3 does not intersect the x-axis.
To determine the number of times the graph of 2x^2 - 2x + 3 intersects the x-axis, we need to find the number of solutions to the equation 2x^2 - 2x + 3 = 0.
To find the solutions, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 2, b = -2, and c = 3. Plugging these values into the quadratic formula, we have:
x = (-(-2) ± √((-2)^2 - 4(2)(3))) / (2(2))
= (2 ± √(4 - 24)) / 4
= (2 ± √(-20)) / 4
Since the term inside the square root is negative, i.e., √(-20), we know that there are no real solutions to the equation. This means that the graph of 2x^2 - 2x + 3 does not intersect the x-axis.
In summary, the graph of 2x^2 - 2x + 3 does not intersect the x-axis, so it does not intersect the x-axis any number of times.