What are the vertex and x-intercepts of the graph of the function given below? y = x2 - 2x - 35
A. Vertex: (1, -25); x-intercepts: (
6,0) and (-4,0)
B. Vertex: (7,5); x-intercepts: (7,0) and (8,0)
C. Vertex: (0,0); x-intercepts: (-4,0) and (-5,0)
D. Vertex: (1, -36); x-intercepts: (7,0) and (-5,0)

D

Step-by-step explanation:

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

= -

y = x² - 2x - 35 ← is in standard form

with a = 1 and b = - 2 , thus

= - = 1

Substitute x = 1 into y for corresponding coordinate of y

y = 1² - 2(1) - 35 = 1 - 2 - 35 = - 36

vertex = (1, - 36 )

To find the x- intercepts let y = 0, that is

x² - 2x - 35 = 0

Consider the factors of the constant term (- 35) which sum to give the coefficient of the x- term (- 2)

The factors are - 7 and + 5, since

- 7 × 5 = - 35 and - 7 + 5 = - 2, thus

(x - 7)(x + 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 5 = 0 ⇒ x = - 5

x- intercepts are (7, 0 ) and (- 5, 0 )

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: