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High School Math : Algebra II

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Example Questions

Example Question #341 : Algebra Ii

Solve using the quadratic formula:

2x^2+2x+3=0

Possible Answers:

$x= \frac{-1 \pm i\sqrt{5}}{3}$

$x= \frac{-2 \pm i\sqrt{5}}{3}$

$x= \frac{-1 \pm i\sqrt{5}}{2}$

$x= \frac{-3 \pm i\sqrt{5}}{2}$

$x= \frac{-2 \pm i\sqrt{5}}{2}$

Correct answer:

$x= \frac{-1 \pm i\sqrt{5}}{2}$

Explanation:

Use the quadratic formula to solve:

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

a = 2

b = 2

c = 3

$x = \frac{-(2) \pm \sqrt{(2)^2-4(2)(3)}}{2(2)}$

$x = \frac{-2 \pm \sqrt{-20}}{4}$

$x = \frac{-2 \pm 2i\sqrt{5}}{4}$

$x = \frac{-1 \pm i\sqrt{5}}{2}$

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Example Question #91 : Intermediate Single Variable Algebra

Solve using the quadratic formula:

2a^2-5a+4=0

Possible Answers:

$a=\frac{4 \pm i\sqrt{7}}{4}$

$a=\frac{6 \pm i\sqrt{7}}{4}$

$a=\frac{3 \pm i\sqrt{7}}{4}$

$a=\frac{7 \pm i\sqrt{7}}{4}$

$a=\frac{5 \pm i\sqrt{7}}{4}$

Correct answer:

$a=\frac{5 \pm i\sqrt{7}}{4}$

Explanation:

Use the quadratic formula to solve:

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

a = 2

b = -5

c = 4

$a = \frac{-(-5) \pm \sqrt{(-5)^2-4(2)(4)}}{2(2)}$

$a = \frac{5 \pm \sqrt{-7}}{4}$

$a = \frac{5 \pm i\sqrt{7}}{4}$

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Example Question #92 : Intermediate Single Variable Algebra

Solve using the quadratic formula:

ax^2+bx+3b=0

Possible Answers:

$x=\frac{b \pm \sqrt{b^2-12ab}}{a}$

$x=\frac{b \pm \sqrt{b^2-12ab}}{2a}$

$x=\frac{-b \pm \sqrt{b^2-8ab}}{2a}$

$x=\frac{-b \pm \sqrt{b^2-12ab}}{a}$

$x=\frac{-b \pm \sqrt{b^2-12ab}}{2a}$

Correct answer:

$x=\frac{-b \pm \sqrt{b^2-12ab}}{2a}$

Explanation:

Use the quadratic formula to solve:

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

a = a

b = b

c = 3b

$x = \frac{-(b) \pm \sqrt{(b)^2-4(a)(3b)}}{2(a)}$

$x = \frac{-b \pm \sqrt{b^2-12ab}}{2a}$

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Example Question #93 : Intermediate Single Variable Algebra

Solve using the quadratric formula:

bx^2+acx+c=0

Possible Answers:

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

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

$x=\frac{-ac\sqrt{a^2c^2-2bc}}{2b}$

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

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

Correct answer:

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

Explanation:

Use the quadratic formula to solve:

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

a = b

b = ac

c = c

$x = \frac{-(ac) \pm \sqrt{(ac)^2-4(b)(c)}}{2(b)}$

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

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Example Question #341 : Algebra Ii

A baseball that is thrown in the air follows a trajectory of h(t)= -4t^2 +12t+6 , where h(t) is the height of the ball in feet and is the time elapsed in seconds. How long does the ball stay in the air before it hits the ground?

Possible Answers:

Between 2.5 and 3 seconds

Between 4 and 4.5 seconds

Between 3 and 3.5 seconds

Between 2 and 2.5 seconds

Between 3.5 and 4 seconds

Correct answer:

Between 3 and 3.5 seconds

Explanation:

To solve this, we look at the equation h(t)=0 .

Setting the equation equal to 0 we get 0= -4t^2 +12t+6 .

Once in this form, we can use the Quadratic Formula to solve for .

The quadratic formula says that if 0= -ax^2 +bx+c , then

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

Plugging in our values:

$t= \frac{-12\pm\sqrt{(12^2-4(-4)(6)}}{2(-4)}=\frac{-12\pm \sqrt{240}}{-8}= \frac{12\pm15.5}{8}$

Therefore t=3.4375 or -.4375 and since we are looking only for positive values (because we can't have negative time), 3.4375 seconds is our answer.

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Example Question #1 : Solving Quadratic Inequalities

Solve the quadratric inequality:

$y\geq -x^2+10x-21$

Possible Answers:

$x\leq2 , x\geq5$

$x\leq3 , x\geq7$

$x\leq4 , x\geq8$

$x\leq1 , x\geq4$

$x\leq5 , x\geq9$

Correct answer:

$x\leq3 , x\geq7$

Explanation:

Factor and solve.

$y\geq -x^2+10x-21$

$y\leq x^2-10x+21$

Since the equation is less than or equal to, you know the inequality will be OR, not AND.

$y\leq (x-7)(x-3)$

$x\leq3$ or $x\geq7$

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Example Question #2 : Solving Quadratic Inequalities

Solve the following quadratic inequality:

$y\leq x^2+4x+3$

Possible Answers:

$x\leq -2, x\geq -1$

$x\leq -4, x\geq -2$

$x\leq -3, x\geq -1$

$x\leq -4, x\geq -1$

$x\leq -3, x\geq -2$

Correct answer:

$x\leq -3, x\geq -1$

Explanation:

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND.

$y\leq x^2+4x+3$

$y\leq (x+3)(x+1)$

$x\leq-3$ or $x\geq -1$

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Example Question #41 : Solving Quadratic Equations

Solve the following quadratic inequality:

$y\leq -x^2+6x+5$

Possible Answers:

$3-\sqrt{13}\leq x \leq 3+\sqrt{13}$

$3-\sqrt{10}\leq x \leq 3+\sqrt{10}$

$3-\sqrt{14}\leq x \leq 3+\sqrt{14}$

$3-\sqrt{15}\leq x \leq 3+\sqrt{15}$

$3-\sqrt{11}\leq x \leq 3+\sqrt{11}$

Correct answer:

$3-\sqrt{14}\leq x \leq 3+\sqrt{14}$

Explanation:

Use the quadratic formula to solve.

$y\leq -x^2+6x+5$

$y\geq x^2-6x-5$

Since the inequality is greater than or equal to, we know the inequality will be AND, not OR.

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

a=1

b=-6

c=-5

$x = \frac{-(-6) \pm \sqrt{(-6)^2-4(1)(-5)}}{2(1)}$

$x= \frac{6 \pm \sqrt{56}}{2}$

$x= 3 \pm \sqrt{14}$

$3-\sqrt{14}\leq x \leq 3+\sqrt{14}$

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Example Question #1 : Understanding Rational Expressions

Solve:

If varies directly as , and x=7 when y=21 , find when y=-5 .

Possible Answers:

$x=\frac{-1}{3}$

$x=\frac{-7}{3}$

$x=\frac{-11}{3}$

$x=\frac{-13}{3}$

$x=\frac{-5}{3}$

Correct answer:

$x=\frac{-5}{3}$

Explanation:

The formula for a direct variation is:

$\frac{x_1}{x_2}=\frac{y_1}{y_2}$

Plugging in our values, we get:

$\frac{7}{x}=\frac{21}{-5}$

21x=-35

$x= \frac{-5}{3}$

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Example Question #2 : Understanding Rational Expressions

If two boxes have the same depth and capacity, the length is inversely proportional to the width. One box is $60\ cm$ long and $40\ cm$ wide. A second box (same depth and capacity) is $5\ cm$ long. How wide is it?

Possible Answers:

$460\ cm$

$480\ cm$

$470\ cm$

$450\ cm$

$490\ cm$

Correct answer:

$480\ cm$

Explanation:

The formula for an indirect variation is:

$\frac{x_1}{x_2}=\frac{y_2}{y_1}$

Plugging in our values, we get:

$\frac{60\ cm}{5\ cm}=\frac{y}{40\ cm}$

$5y=2400\ cm$

$y=480\ cm$

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High School Math : Algebra II

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #341 : Algebra Ii

Example Question #91 : Intermediate Single Variable Algebra

Example Question #92 : Intermediate Single Variable Algebra

Example Question #93 : Intermediate Single Variable Algebra

Example Question #341 : Algebra Ii

Example Question #1 : Solving Quadratic Inequalities

Example Question #2 : Solving Quadratic Inequalities

Example Question #41 : Solving Quadratic Equations

Example Question #1 : Understanding Rational Expressions

Example Question #2 : Understanding Rational Expressions

All High School Math Resources

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