Discriminants and Quadratic Eq

The standard quadratic equation is given as: ax^2 + bx + c = 0 , where a, b, and c are real numbers and a > 0. The quadratic formula can be used to solve for all solutions of any quadratic equation. If a graph of the quadratic equation crosses the x axis, it has two real number solutions. We use the discriminant of b^2 – 4ac, to find out how many solutions a quadratic equation will have. If the discriminant equals 0, there is only 1 solution (real number); if it is positive there are 2 different real number solutions; if it is negative there are 2 different non-real number solutions.

Write a quadratic equation that has solutions: 5, 10

Discriminants and Quadratic Eq

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 – 4ac. This discriminant can be positive, zero, or negative.

Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.

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