Quadratic Formula

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).

Front

What does 'a' represent in the quadratic equation ax² + bx + c = 0?

Back

'a' is the leading coefficient, which determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

What does 'b' represent in the quadratic equation ax² + bx + c = 0?

Back

'b' is the coefficient of the linear term, which affects the position of the vertex of the parabola along the x-axis.

Front

What does 'c' represent in the quadratic equation ax² + bx + c = 0?

Back

'c' is the constant term, which represents the y-intercept of the parabola.

Front

How do you identify the vertex of a parabola given by the equation y = ax² + bx + c?

Back

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting this value back into the equation to find the y-coordinate.

Front

What is the discriminant in the quadratic formula?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

Solve using the quadratic formula: 2x² - 9x - 35 = 0

Back

x = -5/2, x = 7.

Front

Solve using the quadratic formula: x² + 4x - 40 = -8

Back

x = -8, x = 4.

Front

Use the quadratic formula to find the solutions for y = -x² - 5x + 12

Back

x = -6.77, x = 1.77.

Front

Identify the 'c' value in the equation y = 16x² - 8x - 24

Back

'c' = -24.