Solve the quadratic equation by factoring: $$x^2 - 5x + 6 = 0$$

The factored form is $$(x - 2)(x - 3) = 0$$ , so the solutions are $$x = 2$$ and $$x = 3$$ .

What does it mean if a quadratic function has a minimum value?

A quadratic function has a minimum value if it opens upwards (the coefficient of $$x^2$$ is positive), indicating the lowest point on the graph.

Solve the quadratic equation by factoring: $$x^2 - 4 = 0$$

The factored form is $$(x - 2)(x + 2) = 0$$ , so the solutions are $$x = 2$$ and $$x = -2$$ .

What is the vertex of a quadratic function?

The vertex of a quadratic function is the point where the graph changes direction, located at the coordinates $$(h, k)$$ in the vertex form $$y = a(x - h)^2 + k$$ .

How can you determine the number of real roots of a quadratic equation?

The number of real roots can be determined using the discriminant $$D = b^2 - 4ac$$ : if D > 0, there are 2 real roots; if D = 0, there is 1 real root; if D

What is the standard form of a quadratic function?

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

Solve the quadratic equation by factoring: $$x^2 - 2x - 15 = 0$$

The factored form is $$(x - 5)(x + 3) = 0$$ , so the solutions are $$x = 5$$ and $$x = -3$$ .

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 $$x = -\frac{b}{2a}$$ .

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

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

Solve Quadratics by Factoring Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What are the x-intercepts of a quadratic function?

Back

Tags

CCSS.HSF-IF.C.7A

3.

FLASHCARD QUESTION

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros of a quadratic function, set the function equal to zero and solve for x using factoring, completing the square, or the quadratic formula.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

4.

FLASHCARD QUESTION

Front

What is factoring in the context of quadratic equations?

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

What does it mean if a quadratic function has a maximum value?

Back

Tags

CCSS.HSF-IF.C.7A

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