Characteristics of Quadratics Flashcard

Front

What does the variable c represent in the quadratic equation y=ax²+bx+c?

Back

c represents the y-intercept of the quadratic function.

Front

In which direction does the parabola open if the leading coefficient a is negative?

Back

The parabola opens downward.

Front

How can you determine the direction a parabola opens by examining the coefficient a in the equation y=ax²+bx+c?

Back

If a is positive, the parabola opens upward; if a is negative, it opens downward.

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-image halves, given by the formula x = -b/(2a).

Front

How do you find the y-intercept of a quadratic equation?

Back

The y-intercept can be found by evaluating the function at x=0.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c.

Front

What does the term 'roots' refer to in a quadratic equation?

Back

Roots are the x-values where the quadratic function intersects the x-axis (y=0).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b²-4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

How can you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex, which can be found using the formula y = f(-b/(2a)).