Characteristics of Parabolas

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts are the points where the parabola crosses the x-axis, which can be found by setting the quadratic equation to zero.

Front

What do we call the graph of a quadratic function?

Back

The graph of a quadratic function is called a parabola.

Front

What is the maximum or minimum point of a parabola called?

Back

The maximum or minimum point of a parabola is called the vertex.

Front

In which intervals is a parabola increasing if the vertex is at (1, y)?

Back

The parabola is increasing in the interval (1, ∞).

Front

What is the standard form of a quadratic equation?

Back

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

Front

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

Back

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

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

How can you find the vertex of a parabola given in standard form?

Back

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

Front

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

Back

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

Front

What is the vertex form of a quadratic equation?

Back

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