(Grade 11) Section 2.1 - Working With Quadratic Expressions

1) Evaluate 3(2x+3)² for x = –2

–93

–69

3

147

To evaluate the expression 3(2x+3)2 for x = –2, we substitute x = –2 into the given expression. Plugging in x = –2, we have 3(2(-2)+3)2. Simplifying the expression within the parentheses, we get 3(-4+3)2. Further simplifying, we have 3(-1)2. Squaring -1 gives us 1, so the expression becomes 3(1), which is equal to 3. Therefore, the correct answer is 3.

Explanation

To evaluate the expression 3(2x+3)2 for x = –2, we substitute x = –2 into the given expression. Plugging in x = –2, we have 3(2(-2)+3)2. Simplifying the expression within the parentheses, we get 3(-4+3)2. Further simplifying, we have 3(-1)2. Squaring -1 gives us 1, so the expression becomes 3(1), which is equal to 3. Therefore, the correct answer is 3.

2) Expand and simplify (3x + 4)(2x – 2)

6x^2 + 2x – 8

6x^2–14x–8

6x^2+14x+8

6x^2–8

The given expression is a product of two binomials. To expand and simplify the expression, we can use the distributive property. By multiplying each term in the first binomial by each term in the second binomial, we get: (3x * 2x) + (3x * -2) + (4 * 2x) + (4 * -2). Simplifying this further, we get: 6x^2 - 6x + 8x - 8. Combining like terms, we have: 6x^2 + 2x - 8. Therefore, the answer is 6x^2 + 2x - 8.

Explanation

The given expression is a product of two binomials. To expand and simplify the expression, we can use the distributive property. By multiplying each term in the first binomial by each term in the second binomial, we get: (3x * 2x) + (3x * -2) + (4 * 2x) + (4 * -2). Simplifying this further, we get: 6x^2 - 6x + 8x - 8. Combining like terms, we have: 6x^2 + 2x - 8. Therefore, the answer is 6x^2 + 2x - 8.

3)

Which describes the area of the figure as a simplified polynomial?

–x^2+8x+1

5x^2+3

5x^2+8x+3

8x^2+8x

The correct answer, 5x^2+3, is a simplified polynomial that describes the area of the figure. This polynomial represents a quadratic equation with a leading coefficient of 5 and a constant term of 3. It is the only option that does not include any additional terms or variables, making it the simplest representation of the area of the figure.

Explanation

The correct answer, 5x^2+3, is a simplified polynomial that describes the area of the figure. This polynomial represents a quadratic equation with a leading coefficient of 5 and a constant term of 3. It is the only option that does not include any additional terms or variables, making it the simplest representation of the area of the figure.

4)

Which expression represents the area of the triangle?

(x^2+5x+3) / 2

(2x^2+7x–3) / 2

(2x^2+6x–3) / 2

(2x^2+5x–3)/2

The expression (2x^2+5x–3)/2 represents the area of the triangle. It is derived from the formula for the area of a triangle, which is base multiplied by height divided by 2. In this case, the base is represented by 2x^2+5x–3 and the height is 2. Dividing the product of the base and height by 2 gives us the expression (2x^2+5x–3)/2 as the area of the triangle.

Explanation

The expression (2x^2+5x–3)/2 represents the area of the triangle. It is derived from the formula for the area of a triangle, which is base multiplied by height divided by 2. In this case, the base is represented by 2x^2+5x–3 and the height is 2. Dividing the product of the base and height by 2 gives us the expression (2x^2+5x–3)/2 as the area of the triangle.

5)

A pendant has a radius of x + 10mm. Which expression describes the area of the pendant?

πx^2+20x+100

2πx + 20π

πx^2+20πx+100π

100πx^2

The expression πx^2+20πx+100π describes the area of the pendant. The first term, πx^2, represents the area of the circular part of the pendant with radius x. The second term, 20πx, represents the area of the curved part of the pendant with length x. The third term, 100π, represents the area of the circular part of the pendant with radius 10mm. Adding all these terms together gives us the total area of the pendant.

Explanation

The expression πx^2+20πx+100π describes the area of the pendant. The first term, πx^2, represents the area of the circular part of the pendant with radius x. The second term, 20πx, represents the area of the curved part of the pendant with length x. The third term, 100π, represents the area of the circular part of the pendant with radius 10mm. Adding all these terms together gives us the total area of the pendant.

6) A fish pond has a diameter of x metres. Which expression describes the area of the fish pond?

πx^2

(πx^2)/4

(πx^2)/2

4πx^2

The expression (πx^2)/4 describes the area of the fish pond. This can be determined by using the formula for the area of a circle, which is πr^2, where r is the radius of the circle. Since the diameter of the fish pond is x meters, the radius would be x/2. Substituting this into the formula gives us (π(x/2)^2), which simplifies to (πx^2)/4. Therefore, this expression represents the area of the fish pond.

Explanation

The expression (πx^2)/4 describes the area of the fish pond. This can be determined by using the formula for the area of a circle, which is πr^2, where r is the radius of the circle. Since the diameter of the fish pond is x meters, the radius would be x/2. Substituting this into the formula gives us (π(x/2)^2), which simplifies to (πx^2)/4. Therefore, this expression represents the area of the fish pond.