Graphs of Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What does the coefficient 'a' in a quadratic function determine?

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

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 vertex of a quadratic function?

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 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, which gives the value of c in y = ax² + bx + c.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

What does it mean for a quadratic function to have a maximum value?

Back

A quadratic function has a maximum value when it opens downwards (a < 0), and the vertex is the highest point on the graph.

Front

What does it mean for a quadratic function to have a minimum value?

Back

A quadratic function has a minimum value when it opens upwards (a > 0), and the vertex is the lowest point on the graph.

Front

How can you determine the direction of a parabola?

Back

The direction of a parabola can be determined by the sign of the coefficient 'a': positive means it opens up, negative means it opens down.

Front

What are the zeroes of a quadratic function?

Back

The zeroes (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.