Enter values for a, b, and c to see how the graph changes:
Graph the function y = x² - 4x + 3
Step 1: Identify coefficients: a = 1, b = -4, c = 3
Step 2: Find the vertex: x = -(-4) / (2 * 1) = 2
Step 3: Calculate vertex y: y = (2)² - 4(2) + 3 = -1
Step 4: Find x-intercepts by solving x² - 4x + 3 = 0
(x - 1)(x - 3) = 0 → x = 1, x = 3
Step 5: Find y-intercept: Set x = 0 → y = 3
Graph the function y = 2x² - 3x + 1
Step 1: Identify coefficients: a = 2, b = -3, c = 1
Step 2: Find the vertex: x = -(-3) / (2 * 2) = 0.75
Step 3: Calculate vertex y: y = 2(0.75)² - 3(0.75) + 1 = -0.125
Step 4: Find x-intercepts by solving 2x² - 3x + 1 = 0
Using quadratic formula: x = [3 ± √(9 - 8)] / 4
x = 0.5 or x = 1
Step 5: Find y-intercept: Set x = 0 → y = 1