My assignment is late and i'm stuck on this question! ( explain fully but keep it simple)

an expression is shown below:

f(x) = 2x2 − 3x − 5

part a: what are the x-intercepts of the graph of f(x)? show your work. (2 points)

part b: is the vertex of the graph of f(x) going to be a maximum or minimum? what are the coordinates of the vertex? justify your answers and show your work. (3 points)

part c: what are the steps you would use to graph f(x)? justify that you can use the answers obtained in part a and part b to draw the graph. (5 points)

A)

f(x) = 2x2 − 3x − 5

To find the x intercepts, set the equation to equal 0 and solve for x:

2x^2 - 3x -5 = 0

Factor by grouping:

2x^2 - 5x +2x -5 = 0

x(2x-5) +1(2x-5)=0

(2x-5)(x+1)=0

x= 5/2 and x = -1

X-intercepts = (5/2,0) and (-1,0)

B)

In the given equation a = 2, b = -3 and c = -5

Use those values to find the vertex:

Vertex form is a(x +d)^2 +e

D = b/a^2 = -3/2^2 = -3/4

E = c - b^2/4a = -5 - -3^2/4(2) = -49/8

Replace the letters with their values:

2(x-3/4)^2 - 49/8

The vertex is (3/4, -49/8)

Because the Y value is negative, the vertex is a minimum ( below 0)

C) You would then need to find the Y - intercept by replacing x with 0 in the original equation to get ( 0,-5)

Now you have 4 sets of coordinates to plot on a graph, then connect with a line forming a parabola.

"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:

can you complete your sentence? i could !