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.

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.

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.

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.

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.

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.

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).

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.