Key Features Quadratics

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

How do you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x.

Tags

CCSS.HSF-IF.C.7A

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Tags

CCSS.HSF-IF.C.7A

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 formula x = -b/(2a).

Front

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

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Tags

CCSS.HSF-IF.C.7A

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola and is the y-value of the vertex.

Front

How can you determine if a quadratic function has real x-intercepts?

Back

You can determine this by calculating the discriminant (b² - 4ac); if it is positive, there are 2 real x-intercepts, if zero, 1 real x-intercept, and if negative, none.

Tags

CCSS.HSA-REI.B.4B