For y = ax^2 + bx + c, what does c represent on the graph?

For y = ax^2 + bx + c, what does c represent on the graph?

• A. The x-intercept
• B. The y-intercept
• C. The slope of the tangent at x=0
• D. The axis of symmetry

Answer: (B)

In a quadratic written as y = ax^2 + bx + c, the constant term c is the y-coordinate of the point where the graph crosses the y-axis. When x = 0, the equation gives y = c, so the intercept on the y-axis is (0, c). That’s why c represents the y-intercept. The other ideas don’t fit: the x-intercept happens where y = 0 (that depends on all three coefficients), the slope of the tangent at x = 0 is found from the derivative and equals b, not c, and the axis of symmetry is the vertical line x = -b/(2a). For example, if y = 2x^2 + 3x + 5, the graph crosses the y-axis at y = 5.

In a quadratic written as y = ax^2 + bx + c, the constant term c is the y-coordinate of the point where the graph crosses the y-axis. When x = 0, the equation gives y = c, so the intercept on the y-axis is (0, c). That’s why c represents the y-intercept. The other ideas don’t fit: the x-intercept happens where y = 0 (that depends on all three coefficients), the slope of the tangent at x = 0 is found from the derivative and equals b, not c, and the axis of symmetry is the vertical line x = -b/(2a). For example, if y = 2x^2 + 3x + 5, the graph crosses the y-axis at y = 5.