Question

Find x-intercepts of y = x\(^2\) - 4x + 3.

• A. (0,1) & (0,3)
• B. (1,0) & (3,0)
• C. (1,0) & (2,0)
• D. (0,2) & (0,3)

Hint:

For any equation, to find the x-intercept(s), set y=0. To find the y-intercept(s), set x=0.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The x-intercepts are the points where the graph of the equation crosses the x-axis. At any point on the x-axis, the y-coordinate is 0.
Step 2: Key Formula or Approach:
To find the x-intercepts, we must set y = 0 in the given equation and solve for x.
The equation to solve is a quadratic equation: x\(^2\) - 4x + 3 = 0.
Step 3: Detailed Explanation:
Set y = 0:
\[ x^2 - 4x + 3 = 0 \] This is a quadratic equation that can be solved by factoring. We need to find two numbers that multiply to +3 and add up to -4. These numbers are -1 and -3.
So, we can factor the equation as:
\[ (x - 1)(x - 3) = 0 \] For the product of two factors to be zero, at least one of the factors must be zero.
Case 1: x - 1 = 0 \(\implies\) x = 1
Case 2: x - 3 = 0 \(\implies\) x = 3
The values of x are 1 and 3. The corresponding y-value is 0 for both.
Therefore, the x-intercepts are the points (1, 0) and (3, 0).
Step 4: Final Answer:
The x-intercepts are (1,0) and (3,0).