How do you solve quadratics using graphing?

Answer 1

Recall that the graph of a linear equation in two variables is a line. The equation

y = ax^2 + bx + c, where a, b, and c are real numbers and a is different than 0 represents a quadratic function. Its graph is a parabola, a smooth and symmetric U-shape.

1. The axis of symmetry is the line that divides the parabola into two matching parts.

Its equation is x = -b/2a

2. The highest or lowest point on a parabola is called the vertex (also called a turning point). Its x-coordinate is the value of -b/2a.

If a > 0, the parabola opens upward, and the vertex is the lowest point on the parabola. The y-coordinate of the vertex is the minimum value of the function.

If a < 0, the parabola opens downward, and the vertex is the highest point on the parabola. The y-coordinate of the vertex is the maximum value of the function.

3. The x-intercepts of the graph of y = ax^2 + bx + c are the real solutions to ax^2 + bx + c = 0.

The nature of the roots of a quadratic function can be determined by looking at its graph.

If you see that there are two x-intercepts on the graph of the equation, then the equation has two real roots.

If you see that there is one x-intercept on the graph of the equation, then the equation has one real roots.

If you see that the graph of the equation never crosses the x-axis, then the equation has no real roots.

The roots can be used further to determine the factors of the equation, as

(x - r1)(x -r2) = 0