Math Flashcard

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 and a ≠ 0.

Front

What are the roots of the quadratic equation q² + 14q + 48 = 0?

Back

The roots of the equation are (-6, -8).

Front

How do you find the roots of a quadratic equation using factoring?

Back

To find the roots using factoring, express the quadratic in the form (x - p)(x - q) = 0, where p and q are the roots.

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.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

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 is at the point (-b/(2a), f(-b/(2a))).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a) that divides the parabola into two mirror-image halves.

Front

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

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 do you determine if a quadratic function has a maximum or minimum value?

Back

If the leading coefficient (a) is positive, the function has a minimum value; if negative, it has a maximum value.

Front

What is the factored form of a quadratic equation?

Back

The factored form is expressed as y = a(x - p)(x - q), where p and q are the roots of the equation.