Algebra Unit 4 Review

Front

What are the x-intercepts?

Back

The x-intercepts are the points where the graph of a function crosses the x-axis. For the function in the question, the x-intercepts are 2 and 4.

Front

A soccer ball is kicked from the ground is modeled by the function h=-16t²+54t. What is the height of the soccer ball 3 seconds after it has been kicked?

Back

To find the height, substitute t=3 into the function: h = -16(3)² + 54(3) = 18 feet.

Front

What is the average rate of change over an interval?

Back

The average rate of change is calculated by the formula (f(b) - f(a)) / (b - a). In this case, the average rate of change is 7/3.

Front

What is the equation of the graph represented by f(x) = (x - 1)² - 5?

Back

This equation represents a parabola that opens upwards with its vertex at (1, -5).

Front

Complete the Square: x² + 6x = 5

Back

The completed square form is (x + 3)² = 14.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c.

Front

What does it mean to complete the square?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve.

Front

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

Back

The vertex of a parabola in standard form f(x) = ax² + bx + c can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation: if positive, two real roots; if zero, one real root; if negative, no real roots.

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.