What is the solution to the equation $$9x^2 - 3 = -152$$ ?

The solution is $$\frac{i\text{sqrt}{149}}{3}$$ .

What is the Intercept Form of the quadratic equation $$y = -x^2 + 6x - 5$$ ?

The Intercept Form is $$y = -(x - 1)(x - 5)$$ .

What is the Vertex Form of the quadratic equation $$y = -x^2 + 8x - 15$$ ?

The Vertex Form is $$y = -(x - 4)^2 + 1$$ .

What is the discriminant in a quadratic equation?

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

What is the vertex of a parabola?

The vertex is the highest or lowest point of the parabola, depending on its orientation.

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

The vertex can be found using the formula $$x = -\frac{b}{2a}$$ .

What is the standard form of a quadratic equation?

The standard form is $$y = ax^2 + bx + c$$ .

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

The leading coefficient determines the direction of the parabola: if positive, it opens upwards; if negative, it opens downwards.

What is the axis of symmetry in a parabola?

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

What is the factored form of a quadratic equation?

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

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

The sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

Math 3 Benchmark 2 Study Guide Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

Back

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

If a quadratic equation cannot be factored, does it have at least one imaginary solution?

Back

False.

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

7.

FLASHCARD QUESTION

Front

What does it mean for a quadratic equation to have imaginary solutions?

Back

Imaginary solutions occur when the discriminant of the equation is negative, indicating no real roots.

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