Changing the value of “b” will move the axis of symmetry of the parabola from side to side; increasing b will move the axis in the opposite direction. Changing the value of “c” will move the vertex of the parabola up or down and “c” is always the value of the y-intercept.

Since y = mx + b is an equation of degree one, the quadratic function, y = ax2 + bx + c represents the next level of algebraic complexity.

So the y-intercept of any parabola is always at (0,c).

The “c” value represents the y-intercept, where the parabola crosses the y-axis. This picture supports this, the “c” value in the equation is 3, and that’s exactly where the parabola intercepts with the y-axis.

As we can see from the graph, changing c affects the vertical shift of the graph. When c > 0, the graph shifts up c units. When c < 0, the graph shift down c units.

Standard Form: the standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers. The standard form of a line is just another way of writing the equation of a line.

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it’s pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations.

The Quadratic Formula uses the “a”, “b”, and “c” from “ax2 + bx + c”, where “a”, “b”, and “c” are just numbers; they are the “numerical coefficients” of the quadratic equation they’ve given you to solve.

You could simply write it as y = 5x. Thus if we compare to the standard form equation y = ax + b, a=5 and b=0. Thus the y-inercept is zero.