How do you determine the roots of the equation $$2x^2 + 2x - 12 = 0$$ ?

Use the quadratic formula: $$x = \frac{{-2 \pm \sqrt{{2^2 - 4(2)(-12)}}}}{{2(2)}}$$ , which simplifies to the roots $$x = 2$$ and $$x = -3$$ .

What is a root of the equation $$x^2 + 4x + 3 = 0$$ ?

One of the roots is $$x = -1$$ .

What does it mean for a function to have a minimum value?

A function has a minimum value at a point where the function's output is less than or equal to the output at all other points in its domain.

How do you find the vertex of a quadratic function?

The vertex of a quadratic function $$f(x) = ax^2 + bx + c$$ can be found using the formula $$x = -\frac{b}{2a}$$ .

What is the significance of the discriminant in a quadratic equation?

The discriminant, given by $$b^2 - 4ac$$ , determines the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, no real roots.

What is the range of a quadratic function that opens upwards?

The range of a quadratic function that opens upwards is from the minimum value to infinity.

How do you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, and intercepts, then plot points and draw a parabolic curve.

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

What is the vertex form of a quadratic function?

The vertex form of a quadratic function is $$f(x) = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

How do you identify the maximum or minimum of a quadratic function?

The maximum or minimum value of a quadratic function occurs at the vertex, determined by the sign of the coefficient 'a': if 'a' is positive, it has a minimum; if negative, a maximum.

QSE2 Review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the minimum value of a function on a given interval?

Back

The minimum value of a function on an interval is the smallest output value of the function within that interval.

5.

FLASHCARD QUESTION

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers unless specified otherwise.

6.

FLASHCARD QUESTION

Front

How do you convert a quadratic equation to standard form?

Back

7.

FLASHCARD QUESTION

Front

Back

The coefficients are: a = 4, b = -8, c = -3.

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