100 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!! PLEASE SHOW STEPS TO ALL PARTS

2 answers:

8 0

Answer:

Step-by-step explanation:

Part A: the x-intercepts are -3/2 and 5/2

2x + 3 = 0 --------> 2x = -3 ----------> x = $\frac{-3}{2}$

2x - 5 = 0 ---------> 2x = 5 -----------> x = $\frac{5}{2}$

Part B: the parabola is a minimum, the vertex is (7/8,-289/16)

f(x)=ax^2+bx+c

if a>0, then the parabola opens up and the vertex is a minimum

a<0 then the parabola opens down and the vertex is a max

the x value of the vertex in f(x)=ax^2+bx+c= is -b/(2a)

the y value of the vertex is f(-b/(2a))

f(x) = 4 $x^{2}$ - 7x - 15

a = 4

b = -7

-b/2a=-(7)/(2*4)=7/8

f(7/8) = 4 $(7/8)^{2}$ - 7(7/8) - 15

f(7/8) = 49/16 - 49/8 - 15

f(7/8) = -289/16

Part C:

the vertex is minimum and the graph goes through the x intercepts
plug in x values to get the y value (EX: choose 0 for x, and you'll get -15 for y, so you would plot the point at (0, -15). you could plug in 1 for x, and get -18 for y, plotting the point (1, -18) )