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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Understanding Vertical And Horizontal Lines

Which of the following is a vertical line?

Possible Answers:

y = 3x + 2

$y = \frac{1}{x}$

y = x

y = 4

x = 3

Correct answer:

x = 3

Explanation:

A vertical line is one in which the values can vary. Namely, there is only one possible value for , and can be any number. Thus, by this description, the only vertical line listed is x = 3 .

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Example Question #2 : Understanding Vertical And Horizontal Lines

Which of the following has a slope of 0?

Possible Answers:

$y = 3^{x}$

x = 0

y = x

y = 10

$y = \frac{1}{x}$

Correct answer:

y = 10

Explanation:

A line with a slope of zero will be horizontal. A horizontal line has only one possible value for , and can be any value.

Thus, the only given equation which fits this description is y = 10 .

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Example Question #812 : Algebra Ii

Which of the following is a vertical line?

Possible Answers:

x = 2

y = 3x + 3

y = -x + 2

y = 0

y = 6

Correct answer:

x = 2

Explanation:

A vertical line has infinitely many values of but only one value of . Thus, vertical lines are of the form x = c , where is a real number. The only equation of this form is x = 2 .

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Example Question #1671 : High School Math

Solve for the - and - intercepts:

5x-2y=11

Possible Answers:

$\left ( -\frac{11}{5},0\right)\ and \left ( 0,-\frac{11}{2}\right)$

$\left ( -\frac{11}{5},0\right)\ and \left ( 0,\frac{11}{2}\right)$

$\left ( \frac{11}{5},0\right)\ and \left ( 0,\frac{11}{2}\right)$

$\left ( \frac{11}{5},0\right)\ and \left ( 0,-\frac{11}{2}\right)$

Correct answer:

$\left ( \frac{11}{5},0\right)\ and \left ( 0,-\frac{11}{2}\right)$

Explanation:

To solve for the -intercept, set to zero and solve for :

5x-2y=11

5x-2(0)=11

5x=11

$x=\frac{11}{5}$

To solve for the -intercept, set to zero and solve for :

5x-2y=11

5(0)-2y=11

-2y=11

$y=-\frac{11}{2}$

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Example Question #1672 : High School Math

Solve:

x+3y=10

-2x+y=1

Possible Answers:

(3,-2)

Infinitely many solutions

(-2,1)

No solutions

(1,3)

Correct answer:

(1,3)

Explanation:

Use substution to solve this problem:

x+3y=10 becomes x=10-3y and then is substituted into the second equation. Then solve for :

-2(10-3y)+y=1 , so y=3 and x=1 to give the solution (1,3) .

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Example Question #1673 : High School Math

Write 2x+7y=8 in slope-intercept form.

Possible Answers:

$y=\frac{2}{7}x-\frac{8}{7}$

$y=\frac{2}{7}x+\frac{8}{7}$

$y=\frac{-2}{7}x-\frac{8}{7}$

$y=\frac{-2}{7}x+\frac{8}{7}$

Correct answer:

$y=\frac{-2}{7}x+\frac{8}{7}$

Explanation:

Slope-intercept form is y=mx+b .

2x+7y=8

7y=-2x+8

$y=\frac{-2}{7}x+\frac{8}{7}$

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Example Question #11 : Graphing Functions

Based on the figure below, which line depicts a quadratic function?

Possible Answers:

Red line

Green line

Blue line

Purple line

None of them

Correct answer:

Red line

Explanation:

A parabola is one example of a quadratic function, regardless of whether it points upwards or downwards.

The red line represents a quadratic function and will have a formula similar to $\small {f(x)=ax^2+bx+c}$ .

The blue line represents a linear function and will have a formula similar to $\small {f(x)=ax+b$ .

The green line represents an exponential function and will have a formula similar to $\small {f(x)=ax^b}$ .

The purple line represents an absolute value function and will have a formula similar to $\small {f(x)=\left |ax+b \right |}.$ .

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Example Question #21 : Functions And Graphs

Which of the following functions represents a parabola?

Possible Answers:

$f(x) = x^{2} - 9$

$f(x) = \frac{4x^{2}}{x^{3}}$

f(x) = 5

$f(x) = x^{2} - y^{2}$

f(x) = x

Correct answer:

$f(x) = x^{2} - 9$

Explanation:

A parabola is a curve that can be represented by a quadratic equation. The only quadratic here is represented by the function $f(x) = x^{2} - 9$ , while the others represent straight lines, circles, and other curves.

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Example Question #1 : Circle Functions

Find the radius of the circle given by the equation:

x^2+4x+y^2-12y=24

Possible Answers:

Correct answer:

Explanation:

To find the center or the radius of a circle, first put the equation in the standard form for a circle: $(x-x_{1})^2+(y-y_{1})^2=r^2$ , where is the radius and $(x_{1},y_{1})$ is the center.

From our equation, we see that it has not yet been factored, so we must do that now. We can use the formula (ax-b)^2=a^2x^2-2abx +b^2 .

a^2x^2=x^2 , so a=1 .

-2abx=4x and a=1 , so -2b=4 and b=-2 .

Therefore, x^2+4x+4=(x+2)^2 .

Because the constant, in this case 4, was not in the original equation, we need to add it to both sides:

x^2+4x+y^2-12y=24

x^2+4x+ 4+y^2-12y=24+4

(x+2)^2+y^2-12y=28

Now we do the same for :

(x+2)^2+y^2-12y+36=28+36

(x+2)^2+(y-6)^2=64

We can now find :

r^2 = 64 = 8

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Example Question #2 : Circle Functions

Find the center of the circle given by the equation:

x^2+y^2-6x+18y=-65

Possible Answers:

$\left ( -8,5 \right )$

$\left ( 5,5 \right )$

$\left ( 6,-18 \right )$

$\left ( 3,-9 \right )$

$\left ( 12,3 \right )$

Correct answer:

$\left ( 3,-9 \right )$

Explanation:

To find the center or the radius of a circle, first put the equation in standard form: $(x-x_{1})^2+(y-y_{1})^2=r^2$ , where is the radius and $(x_{1},y_{1})$ is the center.

From our equation, we see that it has not yet been factored, so we must do that now. We can use the formula (ax-b)^2=a^2x^2-2abx +b^2 .

a^2x^2=x^2 , so a=1 .

-2abx=-6x and a=1 , so -2b=-6 and b=3 .

This gives x^2-6x+9=(x-3)^2 .

Because the constant, in this case 9, was not in the original equation, we must add it to both sides:

x^2-6x+y^2+18y=-65

x^2-6x+9+y^2+18y=-65+9

(x-3)^2+y^2+18y=-56

Now we do the same for :

(x-3)^2+y^2+18y+81=-56+81

(x-3)^2+(y+9)^2=25

We can now find the center: (3, -9)

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All High School Math Resources

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #2 : Understanding Vertical And Horizontal Lines

Example Question #2 : Understanding Vertical And Horizontal Lines

Example Question #812 : Algebra Ii

Example Question #1671 : High School Math

Example Question #1672 : High School Math

Example Question #1673 : High School Math

Example Question #11 : Graphing Functions

Example Question #21 : Functions And Graphs

Example Question #1 : Circle Functions

Example Question #2 : Circle Functions

All High School Math Resources

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