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2 answers:
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Step-by-step explanation:
The area of a square is
where s is the side length.
It is given that the smaller square side length is s so that means the area of that smaller square is the formula above.
The longer square is twice the side length of the side length of the smaller square.
Since all squares have equal sides, that means all the side are twice than the smaller square sides.
We can represent that larger square area by
(4s) squared
To find how many smaller squares it would take to fill the larger square divide the formula by each other.
(4s)÷s squared =4
Part A:
Given parabola (1) to be
, and parabola (2) to be 
Notice that parabola (2) is stretched horizontally by a factor of 13 which is greater than 1. This means that parabola (2) is further away from the x-axis than parabola (1). (i.e. parabola (2) is more 'vertical' than parabola (1).
Therefore, parabola (1) is wider than parabola (2).
Part B:
A parabola open up when the coefficient of the quadratic term (the squared term) is positive and opens down when the coefficient of the quadratic term is negative.
Given parabola (1) to be, and parabola (2) to be
Notice that the coefficient of the quadratic term is positive for parabola (2) and negative for parabola (1), therefore, the parabola that will open down is parabola (1).
Part C:
For any function, f(x), the graph of the function is moved p places to the left when p is added to x (i.e. f(x + p)) and moves p places to the right when p is subtracted from x (i.e. f(x - p)).
Given parabola (1) to be, and parabola (2) to be
Notice that in parabola (1), 12 is added to x, which means that the graph of the parent function is shifted 12 places to the left while in parabola (2), 4 is subtracted from x, which means that the graph of the parent function is shifted 4 places to the right.
Therefore, the parabola that would be furthest left on the x-axis is parabola (1).
Part D:
For any function, f(x), the graph of the function is moved q places up when q is added to the function (i.e. f(x) + q) and moves q places down when q is subtracted from the function (i.e. f(x) - q).
Given parabola (1) to be, and parabola (2) to be
Notice that in parabola (2), 1 is added to the function, which means that the graph of the parent function is shifted 1 place up while in parabola (1), 6 is subtracted from the function, which means that the graph of the parent function is shifted 6 places down.
Therefore, the parabola that would be highest on the y-axis is parabola (2).
Given parabola (1) to be
Notice that parabola (2) is stretched horizontally by a factor of 13 which is greater than 1. This means that parabola (2) is further away from the x-axis than parabola (1). (i.e. parabola (2) is more 'vertical' than parabola (1).
Therefore, parabola (1) is wider than parabola (2).
Part B:
A parabola open up when the coefficient of the quadratic term (the squared term) is positive and opens down when the coefficient of the quadratic term is negative.
Given parabola (1) to be
Notice that the coefficient of the quadratic term is positive for parabola (2) and negative for parabola (1), therefore, the parabola that will open down is parabola (1).
Part C:
For any function, f(x), the graph of the function is moved p places to the left when p is added to x (i.e. f(x + p)) and moves p places to the right when p is subtracted from x (i.e. f(x - p)).
Given parabola (1) to be
Notice that in parabola (1), 12 is added to x, which means that the graph of the parent function is shifted 12 places to the left while in parabola (2), 4 is subtracted from x, which means that the graph of the parent function is shifted 4 places to the right.
Therefore, the parabola that would be furthest left on the x-axis is parabola (1).
Part D:
For any function, f(x), the graph of the function is moved q places up when q is added to the function (i.e. f(x) + q) and moves q places down when q is subtracted from the function (i.e. f(x) - q).
Given parabola (1) to be
Notice that in parabola (2), 1 is added to the function, which means that the graph of the parent function is shifted 1 place up while in parabola (1), 6 is subtracted from the function, which means that the graph of the parent function is shifted 6 places down.
Therefore, the parabola that would be highest on the y-axis is parabola (2).
Answer:
Step-by-step explanation: