Quadratics Characteristics

Front

What is another name for the x-intercepts of a quadratic?

Back

Zeros

Front

What is the domain of the graph of a quadratic function?

Back

The domain of a quadratic function is all real numbers, but for a specific graph, it can be limited to a range, e.g., -3 ≤ x ≤ 3.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function.

Front

How can you determine the number of zeros a quadratic function has?

Back

The number of zeros can be determined using the discriminant (b² - 4ac) from the quadratic formula. If the discriminant is positive, there are 2 zeros; if it is zero, there is 1 zero; if negative, there are no real zeros.

Front

What is the standard form of a quadratic equation?

Back

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

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

What does the term 'parabola' refer to in mathematics?

Back

A parabola is the graph of a quadratic function, which is a U-shaped curve that can open upwards or downwards.

Front

How does the value of 'a' in the quadratic equation affect the graph?

Back

The value of 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola (narrower if |a| is larger, wider if |a| is smaller).

Front

What is the significance of the y-intercept in 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.

Front

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

Back

The x-intercepts can be found by identifying the points where the graph crosses the x-axis, which correspond to the zeros of the function.