Draw a model to represent the polynomial x^2+2x+4
1. A large square is shown. To the right of the large square is a rectangle whose height is the same as the large square but whose width is much more narrow. To the right of the rectangle are four congruent small squares. The squares are arranged in two columns. Each column has two squares with the top square slightly above the bottom square.
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3. Two large congruent squares are shown in a row. To the right of the large squares are four congruent small squares. The small squares are arranged in two columns. Each column has two squares with the top square slightly above the bottom square.
4. none of these
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x^2+2x+4
This polynomial can be represented by a quadratic function that forms a U-shape when graphed. The vertex of this U-shaped curve is located at the point (-1, 3), and the curve opens upwards.
Graphically, the model can be represented as follows:
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Alternatively, using algebra, we can expand the polynomial as follows:
x^2 + 2x + 4 = (x + 1)^2 + 3
This form of the polynomial shows that it is the sum of a perfect square (x+1)^2 and a constant term 3. We can use this form to graph the polynomial as a shifted parabola, with the vertex at (-1, 3), as shown below:
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Draw a model to represent the polynomial x2 + 2x + 4. (1 point)
model aA large square is shown. To the right of the large square is a rectangle whose height is the same as the large square but whose width is much more narrow. To the right of the rectangle are four congruent small squares. The squares are arranged in two columns. Each column has two squares with the top square slightly above the bottom square.
model b
model cTwo large congruent squares are shown in a row. To the right of the large squares are four congruent small squares. The small squares are arranged in two columns. Each column has two squares with the top square slightly above the bottom square.
none of these
The correct model is model b.
Simplify the polynomial.
–3f2 + 4f – 3 + 8f2 + 7f + 1
(1 point)
5f2 – 11f + 2
11f2 + 11f + 2
5f2 + 11f – 2
–5f2 + 11f – 2
Combine like terms to simplify the polynomial:
-3f^2 + 4f - 3 + 8f^2 + 7f + 1 = 5f^2 + 11f - 2
Therefore, the simplified polynomial is 5f^2 + 11f - 2.
The correct answer is: 5f2 + 11f – 2.
Add or subtract.
(2x2 + 6x + 1) + (–7x2 + 2x – 3) (1 point)
5x2 – 4x – 2
–5x2 + 8x – 2
5x2 – 8x + 2
–9x2 – 8x + 2
Add the like terms to simplify the expression:
(2x^2 + 6x + 1) + (-7x^2 + 2x - 3) = -5x^2 + 8x - 2
Therefore, the simplified expression is -5x^2 + 8x - 2.
The correct answer is: -5x2 + 8x – 2.
(3x2 – 7x – 4) – (6x2 – 6x + 1) (1 point)
–3x2 – x –5
–3x2 –13x + 5
9x2 – x + 5
3x2 – 13x – 5