What are the steps to factor the quadratic equation $$2x^2 - 7x + 6 = 0$$ ?

1. Multiply a and c (2 * 6 = 12). 2. Find two numbers that multiply to 12 and add to -7 (-3 and -4). 3. Rewrite the equation as $$2x^2 - 3x - 4x + 6 = 0$$ . 4. Factor by grouping: $$(2x - 3)(x - 2) = 0$$ .

What are the solutions to the equation $$4x^2 = 100$$ ?

The solutions are $$x = ±5$$ .

How do you find the vertex of a quadratic function?

The vertex of a quadratic function in the form $$y = ax^2 + bx + c$$ can be found using the formula $$x = -\frac{b}{2a}$$ .

What is the discriminant of a quadratic equation?

The discriminant is given by $$D = b^2 - 4ac$$ and determines the nature of the roots: if D > 0, there are two real roots; if D = 0, there is one real root; if D

What is the factored form of the quadratic equation $$x^2 - 5x + 6 = 0$$ ?

The factored form is $$(x - 2)(x - 3) = 0$$ .

What is the solution to the equation $$2x^2 = 100$$ ?

The solution is $$x = ±5\sqrt{2}$$ .

How do you check if your factored solutions are correct?

Substitute the solutions back into the original equation to verify that they satisfy the equation.

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

The coefficient a determines the direction of the parabola (upward if a > 0, downward if a

What is the vertex form of a quadratic equation?

The vertex form is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

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

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

Solving Quadratic Equations by Factoring Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to factor a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

What is the zero-product property?

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, first rewrite the equation in standard form, factor it into two binomials, and then set each factor equal to zero to find the solutions.

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.2

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