Unit 4 Review A

Front

What is the first step in solving the equation y = x^2 + 3x - 5 and y = x + 3?

Back

Set the equations equal to each other: x^2 + 3x - 5 = x + 3.

Front

How do you find the time at which the maximum height occurs for the function h(t) = -16t^2 + 20t + 6?

Back

Use the vertex formula t = -b/(2a) where a = -16 and b = 20. This gives t = 0.625 seconds.

Front

What are the solutions when graphing the equations that intersect at points?

Back

The solutions are the points where the graphs intersect, e.g., (-3,-15) and (4,-8).

Front

How do you solve the quadratic equation 2x^2 - 9x - 35 = 0?

Back

Use the quadratic formula or factoring to find the solutions: x = {-5/2, 7}.

Front

What does the graph of price vs profit represent?

Back

It shows the relationship between price and profit, where the maximum profit is the highest point on the graph.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What is the vertex of a parabola given by the equation y = ax^2 + bx + c?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What does it mean for a function to have a maximum height?

Back

It refers to the highest point on the graph of the function, indicating the peak value of the output.

Front

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

Back

Set the function equal to zero and solve for x using factoring or the quadratic formula.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: two real roots, one real root, or two complex roots.