Graphing Quadratic Functions

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented as (0, c) where c is the constant term in the standard form of the quadratic equation.

Tags

CCSS.HSF-IF.C.7A

Front

How can you determine if a parabola opens upwards or downwards?

Back

A parabola opens upwards if the coefficient of x² (a) is positive and downwards if a is negative.

Tags

CCSS.HSF-IF.C.7A

Front

What are the zeros of a quadratic function?

Back

The zeros (or roots) of a quadratic function are the x-values where the graph intersects the x-axis, found by solving the equation ax² + bx + c = 0.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants.

Front

What does the vertex of a parabola represent?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting this value back into the function to find the y-coordinate.

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 equation x = -b/(2a).

Front

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

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

How can you graph a quadratic function?

Back

To graph a quadratic function, identify the vertex, axis of symmetry, y-intercept, and zeros, then plot these points and draw a smooth curve through them.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.