Solve $$x^2 - 4x - 20 = 0$$ by completing the square.

The solutions are $$x = egin{cases} 2 + 2\\sqrt{6} \ 2 - 2\\sqrt{6} \\end{cases}$$ .

What is a quadratic equation?

A quadratic equation is a polynomial equation of degree 2, typically in the form $$ax^2 + bx + c = 0$$ , where a, b, and c are constants and @@a eq 0@@.

What does the discriminant tell us?

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

What is the vertex of a parabola?

The vertex of a parabola represented by the equation $$y = ax^2 + bx + c$$ is the point where the parabola changes direction. It can be found using the formula $$x = -\frac{b}{2a}$$ .

How do you find the axis of symmetry for a parabola?

The axis of symmetry for a parabola given by the equation $$y = ax^2 + bx + c$$ is the vertical line $$x = -\frac{b}{2a}$$ .

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 the factored form of a quadratic equation?

The factored form of a quadratic equation is $$y = a(x - r_1)(x - r_2)$$ , where $$r_1$$ and $$r_2$$ are the roots of the equation.

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 can you determine if a quadratic equation can be factored?

A quadratic equation can be factored if its discriminant is a perfect square, indicating that the roots are rational.

Solving Quadratics ALL METHODS review Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

Back

The x-intercepts are the points where the graph crosses the x-axis, found using the quadratic formula. For this equation, the x-intercepts are (8, 0) and (-4, 0).

Tags

CCSS.HSF-IF.C.7A

3.

FLASHCARD QUESTION

Front

Back

The solutions are x = -8 and x = 4.

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What is completing the square?

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What is the zero product property?

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

Back

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

Tags

CCSS.HSA-REI.B.4B

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