Quadratic Formula & 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) determines the nature of the roots of a quadratic equation. If D > 0, there are 2 real solutions; D = 0 means 1 real solution; D < 0 indicates no real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

If the Discriminant is negative, what can we conclude about the quadratic equation?

Back

If the Discriminant is negative, the quadratic equation has no real solutions and the graph does not intersect the x-axis.

Tags

CCSS.HSA-REI.B.4B

Front

Identify a, b, and c in the equation: 4x² - 8x = 3.

Back

a = 4, b = -8, c = -3.

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

Subtract 3 from both sides to set the equation to zero.

Tags

CCSS.HSA-REI.B.4B

Front

How do you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if the coefficient of x² (a) is positive, and downwards if a is negative.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex form of a quadratic equation?

Back

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

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line that divides the parabola into two mirror images, given by x = -b/(2a).

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on whether it opens upwards or downwards.

Front

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

Back

To find the x-intercepts, set y = 0 and solve the quadratic equation using the Quadratic Formula.

Tags

CCSS.HSF-IF.C.7A