Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions (roots) 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 are the values of a, b, and c in the equation 4x² - 8x = 3?

Back

a = 4, b = -8, c = -3 (after rearranging to 4x² - 8x - 3 = 0).

Front

What does the term 'axis of symmetry' refer to in a parabola?

Back

The axis of symmetry is an imaginary line that divides the parabola into two mirror-image halves and passes through the vertex.

Front

How do you rearrange a quadratic equation to use the Quadratic Formula?

Back

To use the Quadratic Formula, rearrange the equation to the standard form ax² + bx + c = 0.

Tags

CCSS.HSA-REI.B.4B

Front

What is the discriminant in the Quadratic Formula?

Back

The discriminant is the part of the formula under the square root: b² - 4ac. It determines the nature of the roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that there are two distinct real roots for the quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that there is exactly one real root (a repeated root) for the quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that there are no real roots, but two complex roots for the quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation (opening upwards or downwards).

Front

How can you find the vertex of a parabola given in standard form?

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.