Using the Quadratic Formula a

Front

What is the Quadratic Formula?

Back

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

Front

What does the discriminant tell us?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots of a quadratic equation: if > 0, two real roots; = 0, one real root; < 0, no real roots.

Front

Identify the leading coefficient in the equation y = 2x² + 3x + 5.

Back

The leading coefficient is 2.

Front

What are the values of a, b, and c in the equation y = 4x² + 2x - 6?

Back

a = 4, b = 2, c = -6.

Front

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

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

Solve for x using the Quadratic Formula: 3x² - 12x + 9 = 0.

Back

x = 3 (double root).

Front

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

Back

The leading coefficient determines the direction of the parabola: if positive, it opens upwards; if negative, it opens downwards.

Front

Solve for x: x² - 5x + 6 = 0.

Back

x = 2 and x = 3.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

How do you determine if a quadratic equation has real solutions?

Back

Calculate the discriminant (b² - 4ac): if it is non-negative, the equation has real solutions.