# Alg1.7 Quadratic Equations

### Lesson 1

- I can explain the meaning of a solution to an equation in terms of a situation.
- I can write a quadratic equation that represents a situation.

### Lesson 2

- I can recognize the factored form of a quadratic expression and know when it can be useful for solving problems.
- I can use a graph to find the solutions to a quadratic equation but also know its limitations.

### Lesson 3

- I can find solutions to quadratic equations by reasoning about the values that make the equation true.
- I know that quadratic equations may have two solutions.

### Lesson 4

- I can explain the meaning of the “zero product property.”
- I can find solutions to quadratic equations when one side is a product of factors and the other side is zero.

### Lesson 5

- I can explain why dividing by a variable to solve a quadratic equation is not a good strategy.
- I know that quadratic equations can have no solutions and can explain why there are none.

### Lesson 6

- I can explain how the numbers in a quadratic expression in factored form relate to the numbers in an equivalent expression in standard form.
- When given quadratic expressions in factored form, I can rewrite them in standard form.
- When given quadratic expressions in the form of $x^2+bx+c$, I can rewrite them in factored form.

### Lesson 7

- I can explain how the numbers and signs in a quadratic expression in factored form relate to the numbers and signs in an equivalent expression in standard form.
- When given a quadratic expression given in standard form with a negative constant term, I can write an equivalent expression in factored form.

### Lesson 8

- I can explain why multiplying a sum and a difference, $(x+m)(x-m)$, results in a quadratic expression with no linear term.
- When given quadratic expressions in the form of $x^2+bx+c$, I can rewrite them in factored form.

### Lesson 9

- I can rearrange a quadratic equation to be written as $\text {expression in factored form}=0$ and find the solutions.
- I can recognize quadratic equations that have 0, 1, or 2 solutions when they are written in factored form.

### Lesson 10

- I can use the factored form of a quadratic expression or a graph of a quadratic function to answer questions about a situation.
- When given quadratic expressions of the form $ax^2+bx+c$ and $a$ is not 1, I can write equivalent expressions in factored form.

### Lesson 11

- I can recognize perfect-square expressions written in different forms.
- I can recognize quadratic equations that have a perfect-square expression and solve the equations.

### Lesson 12

- I can explain what it means to “complete the square” and describe how to do it.
- I can solve quadratic equations by completing the square and finding square roots.

### Lesson 13

- When given a quadratic equation in which the coefficient of the squared term is 1, I can solve it by completing the square.

### Lesson 14

- I can complete the square for quadratic expressions of the form $ax^2+bx+c$ when $a$ is not 1 and explain the process.
- I can solve quadratic equations in which the squared term coefficient is not 1 by completing the square.

### Lesson 15

- I can use the radical and “plus-minus” symbols to represent solutions to quadratic equations.
- I know why the plus-minus symbol is used when solving quadratic equations by finding square roots.

### Lesson 16

- I can use the quadratic formula to solve quadratic equations.
- I know some methods for solving quadratic equations can be more convenient than others.

### Lesson 17

- I can use the quadratic formula to solve an equation and interpret the solutions in terms of a situation.

### Lesson 18

- I can identify common errors when using the quadratic formula.
- I know some ways to tell if a number is a solution to a quadratic equation.

### Lesson 19

- I can explain the steps and complete some missing steps for deriving the quadratic formula.
- I know how the quadratic formula is related to the process of completing the square for a quadratic equation $ax^2+bx+c=0$.

### Lesson 20

- I can explain why adding a rational number and an irrational number produces an irrational number.
- I can explain why multiplying a rational number (except 0) and an irrational number produces an irrational number.
- I can explain why sums or products of two rational numbers are rational.

### Lesson 21

- I can explain why adding a rational number and an irrational number produces an irrational number.
- I can explain why multiplying a rational number (except 0) and an irrational number produces an irrational number.
- I can explain why sums or products of two rational numbers are rational.

### Lesson 22

- I can identify the vertex of the graph of a quadratic function when the expression that defines it is written in vertex form.
- I know the meaning of the term “vertex form” and can recognize examples of quadratic expressions written in this form.
- When given a quadratic expression in standard form, I can rewrite it in vertex form.

### Lesson 23

- I can find the maximum or minimum of a function by writing the quadratic expression that defines it in vertex form.
- When given a quadratic function in vertex form, I can explain why the vertex is a maximum or minimum.

### Lesson 24

- I can interpret information about a quadratic function given its equation or a graph.
- I can rewrite quadratic functions in different but equivalent forms of my choosing and use that form to solve problems.
- In situations modeled by quadratic functions, I can decide which form to use depending on the questions being asked.