ACT Math : Algebra
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Example Questions
Example Question #1 : How To Graph A Line
What is the distance between (7, 13) and (1, 5)?
None of the answers are correct
12
10
7
5
10
The distance formula is given by d = square root [(x2 – x1)2 + (y2 – y1)2]. Let point 2 be (7,13) and point 1 be (1,5). Substitute the values and solve.
Example Question #1 : How To Graph A Line
What is the slope of this line?
The slope is found using the formula 
We know that the line contains the points (3,0) and (0,6). Using these points in the above equation allows us to calculate the slope.
Example Question #2 : How To Graph A Line
What is the amplitude of the function if the marks on the y-axis are 1 and -1, respectively?
0.5
3π
π
2π
1
1
The amplitude is half the measure from a trough to a peak.
Example Question #3 : How To Graph A Line
What is the midpoint between 
None of the answers are correct
The x-coordinate for the midpoint is given by taking the arithmetic average (mean) of the x-coordinates of the two end points. So the x-coordinate of the midpoint is given by
The same procedure is used for the y-coordinates. So the y-coordinate of the midpoint is given by
Thus the midpoint is given by the ordered pair
Example Question #4 : How To Graph A Line
If the graph has an equation of 
Example Question #2 : Graphing
The equation 
Cannot be determined
IV
II
I
III
III
Plug in 
Thus, 
Plug in 
Now we know that the line passes through the points 
A quick sketch of the two points reveals that the line passes through all but the third quadrant.
Example Question #2 : How To Graph A Line
Refer to the above red line. A line is drawn perpendicular to that line, and with the same 
First, we need to find the slope of the above line.
The slope of a line. given two points 
Set 
The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be 
Example Question #2 : How To Graph A Function
Refer to the above diagram. If the red line passes through the point 
One way to answer this is to first find the equation of the line.
The slope of a line. given two points 
Set 
The line has slope 3 and 
Now substitute 4 for 
Example Question #1 : How To Graph A Quadratic Function
Best friends John and Elliot are throwing javelins. The height of John’s javelin is described as f(x) = -x2 +4x, and the height of Elliot’s javelin is described as f(x) = -2x2 +6x, where x is the horizontal distance from the origin of the thrown javelin. Whose javelin goes higher?
The javelins reach the same height
John’s
Elliot’s
Insufficient information provided
Elliot’s
When graphed, each equation is a parabola in the form of a quadratic. Quadratics have the form y = ax2 + bx + c, where –b/2a = axis of symmetry. The maximum height is the vertex of each quadratic. Find the axis of symmetry, and plug that x-value into the equation to obtain the vertex.
Example Question #2 : How To Graph A Quadratic Function
Where does the following equation intercept the x-axis?
To determine where an equation intercepts a given axis, input 0 for either 
Now solve for 
Note that in its present form, this is a quadratic equation. In this scenario, we must find two factors of 12, that when added together, equal 7. Quickly, we see that 4 and 3 fit these conditions, giving:
Solving for 
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