Algebra: Concepts and Connections EOC Review 2

Front

What is a quadratic function?

Back

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

Front

What does the vertex form of a quadratic function look like?

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.

Front

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

Back

To find the vertex of a quadratic function in standard form f(x) = ax^2 + bx + c, use the formula h = -b/(2a) and then calculate k by substituting h back into the function.

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept is the point where the graph intersects the y-axis, representing the value of the function when x = 0.

Front

What is the x-intercept of a function?

Back

The x-intercept is the point where the graph intersects the x-axis, representing the values of x for which f(x) = 0.

Front

How do you solve a quadratic equation using factoring?

Back

To solve a quadratic equation by factoring, express it in the form (x - p)(x - q) = 0, then set each factor equal to zero to find the solutions x = p and x = q.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation ax^2 + bx + c = 0 and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does it mean for data to be modeled by a quadratic function?

Back

It means that the relationship between the variables can be represented by a parabolic curve, indicating that the rate of change is not constant.

Front

What is the relationship between the coefficients of a quadratic function and its graph?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0), while 'b' and 'c' affect the position and shape of the graph.

Front

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

Back

If the leading coefficient 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.