Find the x-intercepts of the polynomial y = x^2 - 4x + 3
I'm not sure how to approach this -- do I first factor it and then my x intercepts are (#, 0)?
So, for example, factored would be (x - 3)(x - 1)
I set those equal to 0 so my x intercepts would be (3, 0) and (1, 0)
Would that be correct or is there another way to do it?
correct, at the x-intercept, the value of y = 0
other ways:
you could graph it and verify those answers
you could use the quadratic formula
I know how to put the numbers into the quadratic equation, but then what?
You are on the right track! To find the x-intercepts of a polynomial, you need to set the polynomial equal to zero and solve for x. The x-intercepts occur where the polynomial intersects the x-axis, which means that the y-coordinate is zero.
For the given polynomial, y = x^2 - 4x + 3, you can factor it as (x - 3)(x - 1). To find the x-intercepts, you set each factor equal to zero:
x - 3 = 0 and x - 1 = 0
Solving these equations, you get:
x = 3 and x = 1
So, the x-intercepts of the polynomial y = x^2 - 4x + 3 are (3, 0) and (1, 0).
Yes, you are on the right track! To find the x-intercepts of the polynomial y = x^2 - 4x + 3, you need to set y = 0 and solve for x.
One way to find the x-intercepts is by factoring the quadratic equation if it can be factored easily. In this case, the equation y = x^2 - 4x + 3 can be factored as (x - 3)(x - 1).
When you set (x - 3)(x - 1) = 0, you are essentially setting each factor equal to zero.
So, you have two equations:
(x - 3) = 0 and (x - 1) = 0
By solving these equations individually, you find the values of x that make each factor equal to zero. In this case, x = 3 and x = 1.
Thus, the x-intercepts of the polynomial are (3, 0) and (1, 0), which means the graph of the equation crosses the x-axis at those points.
This method works when the equation can be easily factored, but if the equation cannot be factored or it is difficult to factor, you can use other methods to find the x-intercepts. These methods include completing the square, using the quadratic formula, or graphing the equation.