Solving Quadratics Review

Front

What is the Zero-Product Property?

Back

If the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you determine the number of solutions from a quadratic equation's graph?

Back

The number of solutions corresponds to the number of times the graph intersects the x-axis.

Front

What does a discriminant of zero indicate about the solutions of a quadratic equation?

Back

It indicates that there is exactly 1 real solution.

Front

What is the discriminant formula?

Back

The discriminant (D) is given by D = b² - 4ac for a quadratic equation ax² + bx + c = 0.

Front

How many solutions does the equation 4x² + 4x + 1 = 0 have?

Back

It has 1 solution.

Front

Solve the equation x² + 2x - 24 = 0.

Back

x = -6, x = 4.

Front

What are the possible types of solutions for a quadratic equation?

Back

A quadratic equation can have 0, 1, or 2 real solutions.

Front

What does it mean if a quadratic equation has no real solutions?

Back

It means the graph does not intersect the x-axis.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How can you find the vertex of a quadratic equation in standard form?

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)).