What is the factored form of the quadratic expression $$2x^2 + 15x + 18$$ ?

The factored form is $$(2x + 3)(x + 6)$$ .

What are the solutions to the equation $$x^2 - 8x = 14$$ when solved by factoring?

The solutions are $$x = 3$$ and $$x = 0$$ .

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

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

How do you factor the expression $$5n^3 - 10n^2 + 3n - 6$$ by grouping?

Group as $$(5n^2 + 3)(n - 2)$$ .

What is the standard form of a quadratic equation?

The standard form is $$ax^2 + bx + c = 0$$ where a, b, and c are constants.

What is the vertex form of a quadratic function?

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 the vertical line $$x = -\frac{b}{2a}$$ that divides the parabola into two mirror images.

What is the process of factoring a quadratic expression?

To factor a quadratic expression, find two numbers that multiply to ac and add to b, then rewrite and factor.

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 $$\frac{c}{a}$$ .

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

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

DITOMASSO FINAL EXAM REVIEW #1 - AA SUPP 2024 Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

Back

2.

FLASHCARD QUESTION

Front

How do you find the zeros of a quadratic equation?

Back

Set the quadratic equation to zero and solve for x using factoring, completing the square, or the quadratic formula.

3.

FLASHCARD QUESTION

Front

What is the process of factoring by grouping?

Back

Group terms in pairs, factor out the common factors, and then factor out the common binomial.

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What does it mean to complete the square in a quadratic equation?

Back

6.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

7.

FLASHCARD QUESTION

Front

What is a zero of a function?

Back

A zero of a function is a value of x that makes the function equal to zero.

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