In the quadratic equation of the standard form, which is typically given as y = ax2 + bx + c, the coefficients a, b, and c are critical for defining the shape and position of the parabola on a graph.
For the specific quadratic equation:
y = 5x2 + 4x + 2
We can identify the coefficients as follows:
- a (the coefficient of the x2 term) = 5
- b (the coefficient of the x term) = 4
- c (the constant term) = 2
To summarize:
- a = 5
- b = 4
- c = 2
These values indicate that the parabola opens upwards (since a is positive) and has specific points of intersection with the axes, defined by the values of b and c. The b value affects the slope of the quadratic, while the c value represents the y-intercept.