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.

I can find the maximum or minimum of a function by writing, in vertex form, the quadratic expression that defines it.

When given a quadratic function in vertex form, I can explain why the vertex is a maximum or minimum.

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.

I can use the quadratic formula to solve quadratic equations.

I know some methods for solving quadratic equations can be more convenient than others.

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

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.

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 $ax^2+bx+c=0$.

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 the sum or product of two rational numbers is rational.

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 the sum or product of two rational numbers is rational.

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.

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.

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

I can complete the square for quadratic expressions of the form $ax^2+bx+c$, where $a$ 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.

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.

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.

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.

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.

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.

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 when there are none.

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.

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.

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.

I can rearrange a quadratic equation to be written as an expression in factored form equal to zero and find the solutions.

I can recognize the number of solutions for a quadratic equation from the factored form.

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 $ax^2+bx+c$, where $a$ is not 1, I can write equivalent expressions in factored form.