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 y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What are the key features of a quadratic function?

Back

The key features of a quadratic function include the vertex, axis of symmetry, x-intercepts (roots), y-intercept, and the direction of the parabola (opening upwards or downwards).

Front

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

Back

The vertex of a quadratic function in standard form y = ax^2 + bx + c 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 is the significance of the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, representing the solutions to the equation ax^2 + bx + c = 0.

Front

What does the term 'greatest common factor' (GCF) mean?

Back

The greatest common factor (GCF) is the largest positive integer that divides all the given integers without leaving a remainder.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, look for two numbers that multiply to give the product of the coefficient of x^2 and the constant term, and add to give the coefficient of x. Then, rewrite the expression using these factors.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How can you determine the direction in which a parabola opens?

Back

The direction in which a parabola opens is determined by the coefficient 'a' in the quadratic function y = ax^2 + bx + c. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What does the point (5, 246) represent in the context of a quadratic function modeling a baseball's height?

Back

In the context of the problem, the point (5, 246) indicates that after 5 seconds, the baseball reaches a height of 246 feet.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, which occurs when x = 0. It can be found by evaluating the function at x = 0.