ACT Math : How to use the quadratic function
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Example Questions
Example Question #1 : How To Use The Quadratic Function
Two consecutive negative odd numbers have a product of 15. What is the sum of the two numbers?
–4
–8
–10
–6
–12
–8
Define the variables x = first number and x + 2 = second number
The product is x(x + 2) = 15, so we need to solve the quadratic equation x2 + 2x – 15 = 0. Factoring we get (x + 5)(x – 3) = 0, so x = –5 or x = 3. The problem calls for negative numbers, so the answers are –5 and –3 and the sum is –8
Example Question #1 : How To Use The Quadratic Function
What is the difference of the values of x that satisfy
4x2+ 3x – 1 = 0?
4/5
0
5/4
3
5/4
Factor the equation (4x – 1) (x + 1)
The solutions are x = –1 and x = 1/4.
The difference is (1/4) – (–1) = 5/4
Example Question #2 : How To Use The Quadratic Function
2x + y = 1
What is the slope and the y-intercept of the given equation, respectively?
1, 1
2, 1
2, –2
1, 2
–2, 1
–2, 1
You put the equation into slope-intercept form (y = mx + b)
The new equation is y= –2x + 1
m = –2 and b = 1
Example Question #2 : How To Use The Quadratic Function
How many solutions are there to: x2 – 9 = 0
0
2
1
Infinitely many
2
There are two solutions that make the solution true: 3 and –3.
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