Algebra 1 | Unit 6 | Lesson 10: Graphs of Functions in Standard and Factored Forms | Practice Problems

Without graphing, identify the x-intercepts of the graph of f. Explain how you know.

Expand (x-7)(x+3) and use the expanded form to identify the y-intercept of the graph of f.

What are the x-intercepts of the graph of the function defined by (x-2)(2x+1)?

• (-2,0) and (1,0)

Here is a graph that represents a quadratic function. Which expression could define this function?

• (x+3)(x+1)

• (x+3)(x-1)

• (x-3)(x+1)

• (x-3)(x-1)

What is the y-intercept of the graph of the equation y = x^2 - 5x + 4?

An equivalent way to write this equation is y = (x-4)(x-1). What are the x-intercepts of this equation’s graph?

Noah said that if we graph y=(x-1)(x+6), the x-intercepts will be at (1,0) and (-6,0). Explain how you can determine, without graphing, whether Noah is correct.

A company sells a video game. If the price of the game in dollars is p the company estimates that it will sell 20,000 - 500p games. Which expression represents the revenue in dollars from selling games if the game is priced at p dollars?

• (20,000 - 500p) + p

• (20,000 - 500p) - p

Write each quadratic expression in standard form. Draw a diagram if needed.

Is the expression equivalent to x^2 + x + 30? Explain how you know. Is the expression 30 + x - x^2 in standard form? Explain how you know.