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Alg1.7 Quadratic Equations

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

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.

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 $ax^2+bx+c$ 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.

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 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 sums or products of two rational numbers are 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 sums or products of two rational numbers are rational.

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 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.

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.