What is the vertex of the quadratic function y = x^2 - 4x + 3?
Practice Questions
1 question
Q1
What is the vertex of the quadratic function y = x^2 - 4x + 3?
(2, -1)
(2, -4)
(1, 2)
(3, 0)
Step 1: Use the vertex formula x = -b/2a. Here, a = 1, b = -4. Step 2: x = 4/2 = 2. Step 3: Substitute x back: y = 2^2 - 4*2 + 3 = -1. Vertex is (2, -1).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the vertex of the quadratic function y = x^2 - 4x + 3?
Solution: Step 1: Use the vertex formula x = -b/2a. Here, a = 1, b = -4. Step 2: x = 4/2 = 2. Step 3: Substitute x back: y = 2^2 - 4*2 + 3 = -1. Vertex is (2, -1).
Steps: 6
Step 1: Identify the coefficients a and b from the quadratic function y = x^2 - 4x + 3. Here, a = 1 and b = -4.
Step 2: Use the vertex formula x = -b / (2a) to find the x-coordinate of the vertex. Substitute b and a: x = -(-4) / (2 * 1).
Step 3: Calculate the value: x = 4 / 2 = 2. This is the x-coordinate of the vertex.
Step 4: Substitute x back into the original equation to find the y-coordinate. Calculate y = 2^2 - 4*2 + 3.
Step 5: Simplify the equation: y = 4 - 8 + 3 = -1. This is the y-coordinate of the vertex.
Step 6: Combine the x and y coordinates to get the vertex: (2, -1).
