How to use the quadratic function
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ACT Math › How to use the quadratic function
How many solutions are there to: x2 – 9 = 0
2
1
0
Infinitely many
Explanation
There are two solutions that make the solution true: 3 and **–**3.
Two consecutive negative odd numbers have a product of 15. What is the sum of the two numbers?
–4
–8
–10
–6
–12
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
What is the difference of the values of x that satisfy
4_x_2+ 3_x_ – 1 = 0?
0
5/4
4/5
3
Explanation
Factor the equation (4_x_ – 1) (x + 1)
The solutions are x = –1 and x = 1/4.
The difference is (1/4) – (–1) = 5/4
2_x_ + y = 1
What is the slope and the y-intercept of the given equation, respectively?
2, 1
1, 2
–2, 1
1, 1
2, –2
Explanation
You put the equation into slope-intercept form (y = mx + b)
The new equation is y= –2_x_ + 1
m = –2 and b = 1