Unit 8, Lesson 23

Using Quadratic Expressions in Vertex Form to Solve Problems

Algebra 1

Practice

Problem 1

Student Task Statement

Here is a graph of a quadratic function . What is the minimum value of ?

<p>Function on a grid. X axis from negative 20 to 10, by 10’s. Y axis from negative 20 to 20, by 20’s. Origin, O. Parabola opens upward with vertex around negative 10 comma 0.</p>

Practice

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Problem 2

Student Task Statement

The graph that represents has its vertex at .

Explain how we can tell from the expression that -4 is the minimum value rather than the maximum value of .

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Problem 3

Student Task Statement

Each expression here defines a quadratic function. Find the vertex of the graph of the function. Then, state whether the vertex corresponds to the maximum or the minimum value of the function.

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Problem 4

ForLesson 19: Deriving the Quadratic Formula

Student Task Statement

Consider the equation .

Can we use the quadratic formula to solve this equation? Explain or show how you know.
Is it easier to solve this equation by completing the square or by rewriting it in factored form and using the zero product property? Explain or show your reasoning.

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Problem 5

ForLesson 17: Applying the Quadratic Formula (Part 1)

Student Task Statement

Match each equation to the number of solutions it has.

no solutions
1 solution
2 solutions

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Problem 6

ForLesson 20: Rational and Irrational Solutions

Student Task Statement

Which equation has irrational solutions?

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Problem 7

ForLesson 21: Sums and Products of Rational and Irrational Numbers

Student Task Statement

Let represent an irrational number and let represent a nonzero rational number. Decide if each statement is true or false. Explain your thinking.

can be rational.
can be rational.
can be rational.

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Problem 8

ForLesson 17: Changing the Vertex

Student Task Statement

Here are graphs of the equations , , and .

How do the three graphs compare?

A parabola labeled y equals x squared in x y plane, origin O. X axis negative 6 to 8, by 2’s. Y axis negative 8 to 16, by 4s. Opens upward with vertex at the origin. Parabola labeled y equals open parentheses, x minus 3, closed parenthesis, squared. Opens upward with vertex at 3 comma 0. Parabola labeled y equals open parenthesis x minus 3, closed parenthesis, squared, plus seven. Opens upwards with vertex at 3 comma 7.
How does the -3 in affect the graph when compared to ?
How does the +7 in affect the graph when compared to ?

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Problem 9

ForLesson 15: Functions Involving Percent Change

Student Task Statement

Three $5,000 loans have different annual interest rates. Loan A charges 10.5% annual interest, Loan B charges 15.75%, and Loan C charges 18.25%.

If we graph the amount owed as a function of years without payment, what would the three graphs look like? Describe or sketch your prediction.
Use technology to graph each function. According to your graphs, if no payments are made, about how many years will it take for the unpaid balance of each loan to triple?

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Using Quadratic Expressions in Vertex Form to Solve Problems

Practice

Problem 1

Student Task Statement

Problem 2

Student Task Statement

Problem 3

Student Task Statement

Problem 4

Student Task Statement

Problem 5

Student Task Statement

Problem 6

Student Task Statement

Problem 7

Student Task Statement

Problem 8

Student Task Statement

Problem 9

Student Task Statement

Lesson 23 Resources