Properties of Quadratic Graphs

Front

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

Back

A quadratic graph can have either a maximum or minimum value depending on the direction it opens. If it opens upwards, it has a minimum value; if it opens downwards, it has a maximum value.

Front

What is the graph of a quadratic function called?

Back

The graph of a quadratic function is called a Parabola.

Front

If a parabola has a vertex at (-3,2), where is the axis of symmetry?

Back

The axis of symmetry is x = -3.

Front

What is the standard form of a quadratic equation?

Back

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

Front

In which direction does the equation y = -3x² - 7x + 8 open?

Back

The equation opens downwards.

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 whether it opens upwards or downwards.

Front

What does the 'a' in the quadratic equation y = ax² + bx + c determine?

Back

The 'a' value determines the direction of the parabola's opening and its width. If 'a' is positive, it opens upwards; if 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 can you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form y = ax² + bx + c.

Front

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

Back

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