Discriminant and Vertex Form Review

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by the formula b² - 4ac, which helps determine the nature of the roots of the quadratic equation ax² + bx + c = 0.

Front

How do you calculate the discriminant for the equation -2x² − x − 1 = 0?

Back

The discriminant is calculated as b² - 4ac. For this equation, a = -2, b = -1, c = -1. Thus, the discriminant is (-1)² - 4(-2)(-1) = 1 - 8 = -7.

Front

What is the vertex of the parabola represented by the equation y=2(x-3)²+4?

Back

The vertex of the parabola is (3, 4). This is derived from the vertex form of a parabola, y = a(x-h)² + k, where (h, k) is the vertex.

Front

Which discriminant value indicates that a quadratic equation has 2 real rational solutions?

Back

A discriminant value of 16 indicates that the quadratic equation has 2 real rational solutions.

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real solutions; the roots are complex or imaginary.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the significance of the vertex in a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens. It represents the maximum or minimum value of the quadratic function.

Front

How can you determine if a quadratic equation has one real solution?

Back

A quadratic equation has one real solution if the discriminant is zero (b² - 4ac = 0). This means the parabola touches the x-axis at one point.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is y = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

What happens to the graph of a quadratic function when the value of 'a' is positive?

Back

When 'a' is positive, the parabola opens upwards, indicating that the vertex is the minimum point of the graph.