How do you simplify $$\text{√72}$$ ?

$$\text{√72} = 6\text{√2}$$ , since 72 = 36 * 2 and $$\text{√36} = 6$$ .

What are the steps to solve $$5b^2 - 4 = 41$$ by square rooting?

1. Rearrange to $$5b^2 = 45$$ . 2. Divide by 5: $$b^2 = 9$$ . 3. Take the square root: $$b = \text{±}3$$ .

What is the factored form of $$-a^2 - 2a + 24 = 0$$ ?

The factored form is $$-(a + 6)(a - 4) = 0$$ .

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

The solutions are $$x = -7$$ and $$x = 7$$ , found by applying the square root property.

What is the importance of the discriminant in quadratic equations?

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

What does it mean for a quadratic to be in standard form?

A quadratic is in standard form when it is expressed as $$ax^2 + bx + c = 0$$ , where a, b, and c are constants.

How do you identify the vertex of a parabola represented by a quadratic equation?

The vertex can be found using the formula $$x = -\frac{b}{2a}$$ to find the x-coordinate, then substitute back to find the y-coordinate.

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 axis of symmetry in a quadratic function?

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

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

The leading coefficient (a) determines the direction of the parabola: if a > 0, it opens upwards; if a

How do you convert a quadratic equation from standard form to vertex form?

To convert, complete the square on the quadratic expression to express it in the form $$y = a(x - h)^2 + k$$ .

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

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

Solving Quadratics Flashcards

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1.

FLASHCARD QUESTION

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What is a quadratic equation?

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2.

FLASHCARD QUESTION

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What does it mean to solve a quadratic equation by factoring?

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3.

FLASHCARD QUESTION

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What is the square root property in solving quadratics?

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4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

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6.

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7.

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