Key Features of Quadratics

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, represented as (0, c) in the equation y = ax^2 + bx + c.

Tags

CCSS.HSF-IF.C.7A

Front

What do you call the graph of quadratic functions?

Back

The graph of quadratic functions is called a parabola.

Tags

CCSS.HSF-IF.C.7A

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c.

Front

What is the vertex of a parabola?

Back

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

Front

What is the difference between maximum and minimum in a quadratic function?

Back

Maximum refers to the highest point of the parabola (opens downwards), while minimum refers to the lowest point (opens upwards).

Front

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

Back

You can determine this by looking at the coefficient 'a' in the standard form; if 'a' is negative, it has a maximum; if positive, it has a minimum.

Front

What is the axis of symmetry in a parabola?

Back

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

Front

What are the roots of a quadratic equation?

Back

The roots (or zeros) are the values of x where the graph intersects the x-axis, found by solving the equation y = 0.

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.

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant tell you about a quadratic equation?

Back

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

Tags

CCSS.HSA-REI.B.4B