Quadratic Formula and Discriminant

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B

Front

What does the Discriminant tell us?

Back

The Discriminant (D = b² - 4ac) indicates the nature of the roots of a quadratic equation. If D > 0, there are two distinct real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

How do you determine the number of solutions using the Discriminant?

Back

Calculate the Discriminant (D = b² - 4ac). If D > 0, there are two solutions; if D = 0, there is one solution; if D < 0, there are no solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of a negative Discriminant?

Back

A negative Discriminant indicates that the quadratic equation has no real solutions, meaning the graph does not intersect the x-axis.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if a quadratic opens upwards?

Back

A quadratic opens upwards if the coefficient of x² (a) is positive. This means the vertex is a minimum point.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if a quadratic opens downwards?

Back

A quadratic opens downwards if the coefficient of x² (a) is negative. This means the vertex is a maximum point.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function. It can be found using the formula (-b/(2a), f(-b/(2a))).

Front

How can you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x, often using the Quadratic Formula.

Tags

CCSS.HSA-REI.B.4B

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a).

Front

What is a real solution in the context of quadratic equations?

Back

A real solution is a value of x that satisfies the quadratic equation and corresponds to a point where the graph intersects the x-axis.