Solve the quadratic equation by factoring: $$a^2 + 10a + 21 = 0$$

The solutions are $$-3$$ and $$-7$$ .

What is the quadratic formula?

The quadratic formula is $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ .

What is the discriminant in a quadratic equation?

The discriminant is $$b^2 - 4ac$$ and determines the nature of the roots.

What does a positive discriminant indicate?

It indicates that the quadratic has two distinct real roots.

What does a zero discriminant indicate?

It indicates that the quadratic has exactly one real root (a repeated root).

What does a negative discriminant indicate?

It indicates that the quadratic has no real roots (the roots are complex).

How can you check if your solutions to a quadratic are correct?

Substitute the solutions back into the original equation to see if they satisfy it.

What is the vertex of a quadratic function?

The vertex is the highest or lowest point of the parabola represented by the quadratic function.

How do you find the vertex of a quadratic function in standard form?

The vertex can be found using the formula $$(h, k) = \left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right)$$ .

finding solutions to quadratics Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What are the solutions, roots, x-intercepts, and zeros of a quadratic equation?

Back

They are all the same thing; they refer to the values of x where the quadratic equals zero.

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

How do you find the zeros of a quadratic equation?

Back

Set each factor equal to zero and solve for x.

4.

FLASHCARD QUESTION

Front

Back

Make it equal 0 by subtracting 3 from each side.

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

7.

FLASHCARD QUESTION

Front

What does it mean for a quadratic to be factored?

Back

Tags

CCSS.HSA-REI.B.4B

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