Quadratic Formula

Front

What is the Quadratic Formula?

Back

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

Front

What does the 'a' value represent in a quadratic equation?

Back

The 'a' value represents the coefficient of x² in the quadratic equation ax² + bx + c.

Front

What does the 'b' value represent in a quadratic equation?

Back

The 'b' value represents the coefficient of x in the quadratic equation ax² + bx + c.

Front

What does the 'c' value represent in a quadratic equation?

Back

The 'c' value represents the constant term in the quadratic equation ax² + bx + c.

Front

How do you determine the number of zeros (roots) of a quadratic equation?

Back

The number of zeros can be determined using the discriminant (b² - 4ac): if it's positive, there are 2 real roots; if zero, 1 real root; if negative, no real roots.

Front

What is the discriminant in the context of the Quadratic Formula?

Back

The discriminant is the part of the Quadratic Formula under the square root, given by b² - 4ac, which determines the nature of the roots.

Front

How do you solve a quadratic equation using the Quadratic Formula?

Back

To solve using the Quadratic Formula, identify a, b, and c from the equation, substitute them into the formula, and simplify to find the values of x.

Front

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

Back

The vertex of a parabola given by 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 is a vertical line that divides the parabola into two mirror images, given by the equation x = -b/(2a).

Front

What is the significance of the leading coefficient 'a' in a quadratic function?

Back

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