What is the first step in solving $$x^2 + 6x - 13 = 3$$ ?

The first step is to make it equal to 0 by subtracting 3 from both sides, resulting in $$x^2 + 6x - 16 = 0$$ .

What are the roots of the equation $$n^2 + 7n + 15 = 5$$ after factoring?

The roots are $$n = -5$$ and $$n = -2$$ .

What is the factored form of $$x^2 - 11x + 19 = -5$$ ?

The factored form is $$(x - 3)(x - 8) = 0$$ , giving roots $$x = 3$$ and $$x = 8$$ .

How do you find the roots of $$7x(x - 6) = 0$$ using the Zero-Product Property?

Set each factor to zero: $$7x = 0$$ gives $$x = 0$$ , and $$x - 6 = 0$$ gives $$x = 6$$ .

What is the GCF (Greatest Common Factor) in the equation $$7r^2 - 14r = -7$$ ?

The GCF is 7, which can be factored out to simplify the equation.

What does it mean for a quadratic to have two real roots?

A quadratic has two real roots if its discriminant (b^2 - 4ac) is greater than zero.

What is the discriminant of a quadratic equation?

The discriminant is the expression $$b^2 - 4ac$$ that determines the nature of the roots of the quadratic equation.

What is the significance of the coefficients a, b, and c in a quadratic equation?

The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic equation.

How can you check if your factored form is correct?

You can check by expanding the factored form back to the original quadratic equation.

What is the relationship between the roots and the coefficients of a quadratic equation?

The sum of the roots is equal to $$-b/a$$ and the product of the roots is equal to $$c/a$$ .

Solving Quadratics by Factoring (a=1 or GCF)

Flashcard

•

Mathematics

•

9th - 10th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA-REI.B.4B, HSF-IF.C.7A, HSA.APR.B.2

Standards-aligned

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FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

FLASHCARD QUESTION

Front

What does it mean to factor a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

What is the Zero-Product Property?

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

How do you solve a quadratic equation by factoring?

Back

1. Set the equation to zero. 2. Factor the quadratic expression. 3. Apply the Zero-Product Property. 4. Solve for the variable.

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

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