Fast ill give 40 points to whoever answers this
an expression is shown below:
f(x) = 2x2 − x − 10
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)

f(x) = 2x^2 - x - 10

a

2x^2 - x - 10 = 0

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

x = -2 or x = 5/2

x intercepts: (-2,0) and (5/2,0)

b

when the coefficient on x^2 is positive we get a cup - concave up positive.   so the vertex is a minimum.

the vertex of ax^2 + bx + c is -b/2a so here that's

x = )/(2(2)) = 1/4

y = f(1/4) = 2(1/16) - 1/4 - 10 = -81/8

vertex (1/4, -81/8)

justify my answer.   let's complete the square

f(x) = 2(x^2 - (1/2) x) - 10

f(x) = 2(x^2 - (1/2) x + 1/16) - 10 - 2/16

f(x) = 2(x - 1/4)^2 - 81/8

that clearly has a minimum at x=1/4, f(1/4)=-81/8

c

we can plot the three points we have and connect them into a parabola as indicated in the figure.

answer: ay  

fonsi  

dy  

oh

oh no, oh no

oh yeah

diridiri, dirididi daddy  

go

sí, sabes que ya llevo un rato mirándote  

tengo que bailar contigo hoy (dy)  

vi que tu mirada ya estaba llamándome  

muéstrame el camino que yo voy (oh)

tú, tú eres el imán y yo soy el metal  

me voy acercando y voy armando el plan  

solo con pensarlo se acelera el pulso (oh yeah)

ya, ya me está gustando más de lo normal  

todos mis sentidos van pidiendo más  

esto hay que tomarlo sin ningún apuro

despacito  

quiero respirar tu cuello despacito  

deja que te diga cosas al oído  

para que te acuerdes si no estás conmigo

despacito  

quiero desnudarte a besos despacito  

firmo en las paredes de tu laberinto  

y hacer de tu cuerpo todo un manuscrito (sube, sube, sube)

(sube, sube)

x= 3^y

step-by-step explanation: