In standard form, quadratic equations take the form and can be solved in various ways. In general, they are solved for the value(s) of that make the equation equal to Thus, becomes Graphically, all points with a -coordinate of are the -intercepts of the function — or the zeros of the parabola. That means, solving a quadratic equation leads to finding the zeros of the parabola. Since a parabola can have or zeros, a quadratic equation can have or solutions.
Simple quadratic equations take the form and are solved using inverse operations. Once remains on the left-hand side, the equation can be written as where . The value of gives the number of solutions the equation has.
Without solving completely, determine the number of solutions the quadratic equation has.
A quadratic equation can have or real solutions. Without solving completely, it's possible to determine how many just by isolating Here, this means subtracting on both sides of the equation.
Since the equation has real solutions. Since the solutions to a quadratic equation give the zeros of the parabola, we can conclude that the parabola does not intersect the -axis.
The area of a square measures Write a simple quadratic equation to represent the area. Then, determine the side length of the square.