Quad Part 2 test review

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is a value calculated from the coefficients of a quadratic equation in the form ax² + bx + c, given by the formula D = b² - 4ac. It helps determine the nature of the roots.

Front

If the discriminant is greater than 0, what can be said about the solutions of the quadratic equation?

Back

There are 2 distinct real solutions.

Front

If the discriminant is equal to 0, what can be said about the solutions of the quadratic equation?

Back

There is exactly 1 real solution (a repeated root).

Front

If the discriminant is less than 0, what can be said about the solutions of the quadratic equation?

Back

There are no real solutions (the solutions are complex or imaginary).

Front

Calculate the discriminant for the equation: 2x² + 3x + 1 = 0.

Back

D = 3² - 4(2)(1) = 9 - 8 = 1 (positive, so 2 distinct real solutions).

Front

Calculate the discriminant for the equation: x² - 4x + 4 = 0.

Back

D = (-4)² - 4(1)(4) = 16 - 16 = 0 (one repeated real solution).

Front

Calculate the discriminant for the equation: x² + 2x + 5 = 0.

Back

D = 2² - 4(1)(5) = 4 - 20 = -16 (no real solutions).

Front

What does a positive discriminant indicate about the graph of the quadratic function?

Back

The graph intersects the x-axis at two points.

Front

What does a zero discriminant indicate about the graph of the quadratic function?

Back

The graph touches the x-axis at one point (the vertex).

Front

What does a negative discriminant indicate about the graph of the quadratic function?

Back

The graph does not intersect the x-axis (it lies entirely above or below it).