The equations of the functions are y = -4(x + 1)^2 + 2, y = 2(x - 2)^2 + 1 and y = -(x - 1)^2 - 2
<h3>How to determine the functions?</h3>
A quadratic function is represented as:
y = a(x - h)^2 + k
<u>Question #6</u>
The vertex of the graph is
(h, k) = (-1, 2)
So, we have:
y = a(x + 1)^2 + 2
The graph pass through the f(0) = -2
So, we have:
-2 = a(0 + 1)^2 + 2
Evaluate the like terms
a = -4
Substitute a = -4 in y = a(x + 1)^2 + 2
y = -4(x + 1)^2 + 2
<u>Question #7</u>
The vertex of the graph is
(h, k) = (2, 1)
So, we have:
y = a(x - 2)^2 + 1
The graph pass through (1, 3)
So, we have:
3 = a(1 - 2)^2 + 1
Evaluate the like terms
a = 2
Substitute a = 2 in y = a(x - 2)^2 + 1
y = 2(x - 2)^2 + 1
<u>Question #8</u>
The vertex of the graph is
(h, k) = (1, -2)
So, we have:
y = a(x - 1)^2 - 2
The graph pass through (0, -3)
So, we have:
-3 = a(0 - 1)^2 - 2
Evaluate the like terms
a = -1
Substitute a = -1 in y = a(x - 1)^2 - 2
y = -(x - 1)^2 - 2
Hence, the equations of the functions are y = -4(x + 1)^2 + 2, y = 2(x - 2)^2 + 1 and y = -(x - 1)^2 - 2
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Answer:
Step-by-step explanation:
Supplementary angles add up to 180
∠1 + 50 = 180
∠1 = 180 - 50
∠1 = 130
∠3 +50 = 180 {Supplementary}
∠3 = 180 - 50
∠3 =130
⇒∠1 = ∠3 = 130
Answer:
640cm³
Step-by-step explanation:
Length SF = ×2
Volume SF = ×2³ = ×8
Volume of B = 8 × 80 = 640cm³
Answer:
yes , 33^2 + 56^2 = 65^2 and obtuse
Step-by-step explanation:
<h2><u>Question 3</u></h2>
make use of the Pythagoras theorem
which is :
c^2 = a^2 + b^2
where c is the hypotenuse.
now put the values in the equation
65^2 = 56^2 + 33 ^2
the answer is :
<u>yes , 33^2 + 56^2 = 65^2</u>
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<h2><u>Question 4</u></h2>
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note if :
c^2 = a^2 + b^2 ----------- right
c^2 < a^2 + b^2------------ acute
c^2 > a^2 + b^2------------- obtuse
hence :
16 + 30 > 38
therefore its : <u>obtuse </u>
The equation that is equivalent to 15-7x=14 is x=7
