Using the Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients of the quadratic equation ax² + bx + c = 0.

Tags

CCSS.HSA-REI.B.4B

Front

What are the coefficients A, B, and C 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 rearrange the equation 9x² = 4 + 7x to use the quadratic formula?

Back

Rearrange to standard form: 9x² - 7x - 4 = 0.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean to 'complete the square'?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, which makes it easier to solve.

Tags

CCSS.HSA-REI.B.4B

Front

What is the discriminant in the quadratic formula, and what does it indicate?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, two complex roots.

Tags

CCSS.HSA-REI.B.4B

Front

How do you find the vertex of a parabola given by a quadratic equation?

Back

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

Front

What is the significance of the leading coefficient in a quadratic equation?

Back

The leading coefficient (A) determines the direction of the parabola: if A > 0, it opens upwards; if A < 0, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

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

Back

The x-intercepts can be found by solving the quadratic equation ax² + bx + c = 0 using the quadratic formula.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

What is the process to solve the equation 2x² + 7x - 15 = 0 using the quadratic formula?

Back

Identify a = 2, b = 7, c = -15, then apply the quadratic formula: x = (-7 ± √(7² - 4*2*(-15))) / (2*2).

Tags

CCSS.HSA-REI.B.4B

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.