Quadratic Key Features

Front

What is a quadratic function?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0.

Front

What are the key features of a quadratic graph?

Back

The key features of a quadratic graph include the vertex, axis of symmetry, x-intercepts (roots), y-intercept, and the direction of opening (upward or downward).

Front

How do you find the vertex of a quadratic function in standard form?

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 does the axis of symmetry represent in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, and it passes through the vertex.

Front

How can you determine the number of x-intercepts of a quadratic function?

Back

The number of x-intercepts can be determined using the discriminant (b^2 - 4ac) from the quadratic formula. If the discriminant is positive, there are two x-intercepts; if it is zero, there is one; and if it is negative, there are none.

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, and it can be found by evaluating the function at x = 0.

Front

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

Back

The maximum or minimum value of a quadratic function occurs at the vertex. If the parabola opens upward, the vertex represents the minimum value; if it opens downward, it represents the maximum value.

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 using factoring, completing the square, or the quadratic formula.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.