What are the solutions to the equation $$x^2 - 49 = 0$$ ?

The solutions are $$x = -7$$ and $$x = 7$$ .

What is the significance of the leading coefficient in a quadratic equation?

The leading coefficient (the coefficient of $$x^2$$ ) determines the direction of the parabola: if it is positive, the parabola opens upwards; if negative, it opens downwards.

How do you solve the quadratic equation $$x^2 + 6x - 16 = 0$$ using the quadratic formula?

Plugging into the quadratic formula gives $$x = \frac{-6 \\pm \\sqrt{(6)^2 - 4(1)(-16)}}{2(1)}$$ .

What are the final solutions for $$x = \frac{-2 \\pm \\sqrt{100}}{4}$$ ?

The final solutions are $$x = -3$$ and $$x = 2$$ .

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is $$y = ax^2 + bx + c$$ , where $$a$$ , $$b$$ , and $$c$$ are constants.

What is completing the square?

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form $$(x - p)^2 = q$$ .

What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation $$x = -\frac{b}{2a}$$ .

How do you factor a quadratic equation?

To factor a quadratic equation, find two numbers that multiply to $$ac$$ and add to $$b$$ , then rewrite the equation as a product of two binomials.

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

The sum of the roots is equal to $$-\frac{b}{a}$$ and the product of the roots is equal to $$\frac{c}{a}$$ , according to Vieta's formulas.

Quadratic Solutions Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What does it mean if the discriminant is negative?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

How do you find the zeros of a quadratic function?

Back

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

What does it mean for a quadratic to have two solutions?

Back

A quadratic has two solutions when the discriminant is positive, indicating two distinct real roots.

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What is the vertex of a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

Back

Since the discriminant is negative (in this case, -11), there are no real solutions.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

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