Q: Which of the following is the standard form of a quadratic equation?

$$ax^2 + bx + c = 0$$,\ a \neq 0$$

Question 1

Which of the following is the standard form of a quadratic equation?

Accepted Answer

$$ax^2 + bx + c = 0$$,\ a 
eq 0$$

Question 2

Given the quadratic function $$f(x) = 2x^2$ - 5x + 3$$, what are its zeros?

Accepted Answer

$$x = 1$$ and $$x = \frac{3}{2}$$

Question 3

Which principle allows you to conclude that if $$ab = 0$$, then $$a = 0 or$$ $$b = 0$$?

Accepted Answer

Principle of Zero Products

Question 4

Solve the equation $$x^2 - 4 = 0$ using the principle of square roots.

Accepted Answer

$$x = 2 or$$ $$x = -2$$

Question 5

What is the discriminant of the quadratic equation $$3x^2 + 2x - 7 = 0$ and what does it indicate about the solutions?

Accepted Answer

Discriminant is $$64$$, indicating two distinct real solutions.

Question 6

Which method is most appropriate for solving $$x^2 + 6x + 9 = 0$?

Accepted Answer

Factoring

Question 7

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 1.5. $$After how many seconds does the ball reach the ground? (Round to the nearest tenth)

Accepted Answer

$$t \approx 4.2$$

Question 8

Which of the following equations is reducible to quadratic form?

Accepted Answer

$$x^4$$ - $$5x^2 + 4 = 0$

Question 9

If the discriminant $$b^2 - 4ac$ of a quadratic equation is negative, what can you conclude about its solutions?

Accepted Answer

There are two complex conjugate solutions.

Question 10

Solve $$2x^2 - 1 = 3x$ by completing the square.

Accepted Answer

$$x = \frac{3 \pm \sqrt{17}}{4}$$

Question 11

Which of the following is the quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 12

A company models its profit by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of items sold in thousands. For what value of $$x$$ does the company break even?

Accepted Answer

$$x = 2 or$$ $$x = 4$$

Question 13

Which step is NOT part of the process of completing the square?

Accepted Answer

Multiply both sides by the coefficient of $$x^2.$$

Question 14

Given $$x^4$$ - $$5x^2 + 4 = 0$, what substitution can be used to reduce it to quadratic form?

Accepted Answer

Let $$u = x^2$

Question 15

If $$x^2 = 7$, what are the solutions using the principle of square roots?

Accepted Answer

$$x = \sqrt{7} or$$ $$x = -\sqrt{7}$$

Question 16

A quadratic equation $$ax^2 + bx + c = 0$ has only one real solution. What must be true about its discriminant?

Accepted Answer

$$b^2 - 4ac = 0$

Question 17

The number of magazine closures after 2012 is modeled by $$m(x) = 34x^2$ - 59x + 81. In $$what year did the closures reach 99?

Accepted Answer

2014

Question 18

Which of the following is a quadratic function?

Accepted Answer

$$f(x) = 3x^2$ - 2x + 1$$

Question 19

If $$f(x) = ax^2$ + bx + c$$ and $$a \u003e 0$$, what is the shape of the graph of $$f(x)$$?

Accepted Answer

A parabola opening upward

Quadratic Equations, Functions, Zeros, and Models (Section 3.2 Study Notes)

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