parts of a quadratic

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What are the parts of a quadratic function?

Back

The parts of a quadratic function include the coefficients (a, b, c), the vertex, the axis of symmetry, the x-intercepts (roots), and the y-intercept.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upwards or downwards.

Front

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

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x, typically using factoring, completing the square, or the quadratic formula.

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.

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 it mean if a quadratic function has a maximum value?

Back

If a quadratic function has a maximum value, it opens downwards, and the vertex represents the highest point on the graph.

Front

What does it mean if a quadratic function has a minimum value?

Back

If a quadratic function has a minimum value, it opens upwards, and the vertex represents the lowest point on the graph.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

The direction of the parabola is determined by the coefficient 'a': if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.