ACT Math : How to use the quadratic function

Study concepts, example questions & explanations for ACT Math

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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?

Possible Answers:

–12

–8

–4

–10

–6

Correct answer:

–8

Explanation:

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 #2 : How To Use The Quadratic Function

What is the difference of the values of x that satisfy 

4x2+ 3x – 1 = 0?

Possible Answers:

3

4/5

5/4

0

Correct answer:

5/4

Explanation:

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 #3 : How To Use The Quadratic Function

2x + y = 1

What is the slope and the y-intercept of the given equation, respectively?

Possible Answers:

2, 1

2, –2

1, 2

1, 1

–2, 1

Correct answer:

–2, 1

Explanation:

You put the equation into slope-intercept form (y = mx b)

The new equation is y= –2x + 1

= –2 and = 1

Example Question #4 : How To Use The Quadratic Function

How many solutions are there to: x– 9 = 0

Possible Answers:

2

0

1

Infinitely many

Correct answer:

2

Explanation:

There are two solutions that make the solution true: 3 and 3.

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