Quadratic formula

Front

What is the quadratic formula?

Back

The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

Tags

CCSS.HSA-REI.B.4B

Front

What are the coefficients in a quadratic equation?

Back

In a quadratic equation of the form ax² + bx + c = 0, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

How do you determine the 'b' value in a quadratic equation?

Back

The 'b' value is the coefficient of the x term in the standard form of the quadratic equation ax² + bx + c = 0.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant, given by b² - 4ac, indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Tags

CCSS.HSA-REI.B.4B

Front

How can you solve a quadratic equation by taking square roots?

Back

To solve a quadratic equation by taking square roots, isolate the x² term, then take the square root of both sides, remembering to consider both the positive and negative roots.

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex of a parabola represented by the quadratic equation y = ax² + bx + c can be found at the point (h, k), where h = -b/(2a) and k is the value of the function at h.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function in the form y = ax² + bx + c is the vertical line x = -b/(2a), which divides the parabola into two mirror-image halves.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form y = ax² + bx + c to vertex form y = a(x - h)² + k, complete the square to find the vertex (h, k).

Front

What is the relationship between the roots and the coefficients of a quadratic equation?

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.

Tags

CCSS.HSA-REI.B.4B