If y=4x + 3, find the value of y when x = -2

QUESTION 1

The given function is



The domain of this function refers to all values of x for which y is defined.

The given function is defined for all real values of x.

The domain is all real numbers.

The correct answer is A

QUESTION 2

The equation in column 1 is



We obtain the vertex form as follows;









The x-value of the vertex is -1.

The equation in column 2 is



We can also find the x-value of the vertex using the formula,






The correct answer is

B) The value found in column #1 is less than the value found in column #2

QUESTION 3

The height of the ball is modeled by


where t equals the time in seconds and h(t) represents the height of the ball at time t seconds.

The axis of symmetry can be found using the formula,







The correct answer is

A) t=2; it takes 2 seconds to reach maximum height and 2 seconds to fall back to the ground

QUESTION 4

The equation of axis of symmetry is given by the formula,



For the axis of symmetry of a given quadratic function to be zero, then the b-value of quadratic function should be zero.

The only equation from the given options whose b-value is zero is



The axis of symmetry is





The correct answer is C

QUESTION 1

The given function is



The domain of this function refers to all values of x for which y is defined.

The given function is defined for all real values of x.

The domain is all real numbers.

The correct answer is A

QUESTION 2

The equation in column 1 is



We obtain the vertex form as follows;









The x-value of the vertex is -1.

The equation in column 2 is



We can also find the x-value of the vertex using the formula,






The correct answer is

B) The value found in column #1 is less than the value found in column #2

QUESTION 3

The height of the ball is modeled by


where t equals the time in seconds and h(t) represents the height of the ball at time t seconds.

The axis of symmetry can be found using the formula,







The correct answer is

A) t=2; it takes 2 seconds to reach maximum height and 2 seconds to fall back to the ground

QUESTION 4

The equation of axis of symmetry is given by the formula,



For the axis of symmetry of a given quadratic function to be zero, then the b-value of quadratic function should be zero.

The only equation from the given options whose b-value is zero is



The axis of symmetry is





The correct answer is C

#1) A
#2) B
#3) C
#5) A
#7) D
#10) D
#11) D
#14) A
#15) D
#16) A
#19) D

Explanation
#1)  If the data set is linear, the slope will be constant throughout the entire data set.  For data set A, the slope between the first two points is:
m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2
Between the second two points,
m=(4-1)/(5-3) = 3/2
Between the third pairs of points,
m=(7-4)/(7-5) = 3/2

The slope is constant throughout the entire set.  The set is also increasing; as x increases, y increases as well.

#2)  Substituting 4 for y and 1 for x, 
y = (x+1)²
4 = (1+1)² = 2²
9 = (1+2)² = 3²
16 = (1+3)² = 4²
This works for each point, so this is the solution.

#3) Since he runs 10 laps per hour t, this is 10t.  Adding the first lap to this, we get y=10t+1.

#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term.  If the common difference is 2, this means that 2 was added each time.  This only works for choice A.

#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.

#10) The formula for slope is:
m=(y₂-y₁)/(x₂-x₁)

Using the information we're given, we have
3=(d-5)/(4-2)
3=(d-5)/2

Multiply both sides by 2:
3*2 = ((d-5)/2)*2
6 = d-5

Add 5 to both sides:
6+5 = d-5+5
11 = d

#11) Using point slope form,
y-y₁ = m(x-x₁)
y-1 = 3(x--2)
y-1 = 3(x+2)

Using the distributive property,
y-1 = 3*x + 3*2
y-1 = 3x + 6

Add 1 to both sides:
y-1+1 = 3x+6+1
y=3x+7

#14) If two lines are parallel, they have the same slope.  The slope of the given equation is 4; the only one with a slope of 4 is A.

#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped).  The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2.  The only one with this slope is D.

#16)  The two equations are not the same, so there are not infinitely many solutions.  The variables do not both cancel, so there is at least one solution.  This only leaves one solution as the answer.

#19)  Using 1 for 7 and 4 for x, we check each equation.  The only one that comes out correct is D.

#1) A
#2) B
#3) C
#5) A
#7) D
#10) D
#11) D
#14) A
#15) D
#16) A
#19) D

Explanation
#1)  If the data set is linear, the slope will be constant throughout the entire data set.  For data set A, the slope between the first two points is:
m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2
Between the second two points,
m=(4-1)/(5-3) = 3/2
Between the third pairs of points,
m=(7-4)/(7-5) = 3/2

The slope is constant throughout the entire set.  The set is also increasing; as x increases, y increases as well.

#2)  Substituting 4 for y and 1 for x, 
y = (x+1)²
4 = (1+1)² = 2²
9 = (1+2)² = 3²
16 = (1+3)² = 4²
This works for each point, so this is the solution.

#3) Since he runs 10 laps per hour t, this is 10t.  Adding the first lap to this, we get y=10t+1.

#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term.  If the common difference is 2, this means that 2 was added each time.  This only works for choice A.

#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.

#10) The formula for slope is:
m=(y₂-y₁)/(x₂-x₁)

Using the information we're given, we have
3=(d-5)/(4-2)
3=(d-5)/2

Multiply both sides by 2:
3*2 = ((d-5)/2)*2
6 = d-5

Add 5 to both sides:
6+5 = d-5+5
11 = d

#11) Using point slope form,
y-y₁ = m(x-x₁)
y-1 = 3(x--2)
y-1 = 3(x+2)

Using the distributive property,
y-1 = 3*x + 3*2
y-1 = 3x + 6

Add 1 to both sides:
y-1+1 = 3x+6+1
y=3x+7

#14) If two lines are parallel, they have the same slope.  The slope of the given equation is 4; the only one with a slope of 4 is A.

#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped).  The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2.  The only one with this slope is D.

#16)  The two equations are not the same, so there are not infinitely many solutions.  The variables do not both cancel, so there is at least one solution.  This only leaves one solution as the answer.

#19)  Using 1 for 7 and 4 for x, we check each equation.  The only one that comes out correct is D.

Y = -4x + 3
For x = 0, y = -4(0) + 3 = 0 + 3 = 3
For x = 1, y = -4(1) + 3 = -4 + 3 = -1
For x = 2, y = -4(2) + 3 = -8 + 3 = -5
For x = 3, y = -4(3) + 3 = -12 + 3 = -9

Option C is the correct answer.

Y = -4x + 3
For x = 0, y = -4(0) + 3 = 0 + 3 = 3
For x = 1, y = -4(1) + 3 = -4 + 3 = -1
For x = 2, y = -4(2) + 3 = -8 + 3 = -5
For x = 3, y = -4(3) + 3 = -12 + 3 = -9

Option C is the correct answer.