Part 1:
find the vertex, axis of symmetry, domain, and range of the graph of y = −2x^2 − 6x + 1.

part 2:
using complete sentences, explain how you can determine the axis of symmetry, the domain, and range without graphing y = −2x^2 − 6x + 1.

The following are the answers to the questions presented:

Part 1:

Vertex: (−3/ 2, 11/2)

Axis of symmetry = x = -3/2

Domain = all real numbers

Range = y ≤ 11/2

Part 2:

A quadratic equation is symmetrical around its vertex. The equation for the axis of symmetry is x = -3/2 since the equation is in terms of x. Since no value of x is undefined, then the domain of the equation is clearly all real numbers. Since the value of “a” is negative, then that means the y coordinate of the vertex is the maximum value so the range will never get above 11/2. I am hoping that these answers have satisfied your queries and it will be able to help you in your endeavors, and if you would like, feel free to ask another question.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)