Lesson 4.0 Characteristics of Quadratics (pt. 1)

Front

What is the standard equation of a quadratic function?

Back

y = ax² + bx + c, where a, b, and c are constants.

Front

What shape does the graph of a quadratic function form?

Back

A parabola.

Front

What is the vertex of a quadratic function?

Back

The highest or lowest point of the parabola.

Front

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

Back

By looking at the coefficient 'a' in the equation; if 'a' is positive, it has a minimum; if 'a' is negative, it has a maximum.

Front

What is the y-intercept of a quadratic function?

Back

The point where the graph intersects the y-axis, found by setting x = 0.

Front

What does the axis of symmetry in a quadratic function represent?

Back

A vertical line that divides the parabola into two mirror-image halves, given by x = -b/(2a).

Front

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

Back

The discriminant (b² - 4ac) determines the number and type of roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the maximum value of a quadratic function?

Back

The y-coordinate of the vertex when the parabola opens downwards.

Front

What is the minimum value of a quadratic function?

Back

The y-coordinate of the vertex when the parabola opens upwards.

Front

How do you find the roots of a quadratic equation?

Back

By factoring, completing the square, or using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).