What are the vertex and x intercepts of the graph of y=(x+4)(x-2)? select one answer for the vertex and one for the x intercepts.

a. x intercepts (-4,0) ,(2,0)
b. x intercepts (-4,,0)
c. vertex (1,9)
d. vertex (-1,-5)
e. vertex (-1,-9)
f. x intercepts (4,,0)

The x-intercepts points are (-4 , 0) , (2 , 0) ⇒ answer (A)

The vertex point is (-1 , -9) ⇒ answer (E)

Step-by-step explanation:

* Lets revise the quadratic equation

 y = ax² + bx + c

- To find the x-intercepts put y = 0

- To find the vertex use the rule:

# x-coordinate of the vertex of the parabola which represents

  the quadratic function graphically = -b/2a

# To find the y-coordinate substitute the value of the x-coordinate

  of the vertex in the equation

* Lets use these information to solve the problem

∵ y = (x + 4)(x -2)

- To find the x-intercepts let y = 0

∴ (x + 4)( x - 2) = 0 ⇒ put each bracket = 0

∴ x + 4 = 0 and x - 2 = 0

∵ x + 4 = 0 ⇒ subtract 4 from the both sides

∴ x = -4

∵ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

* The x-intercepts points are (-4 , 0) , (2 , 0)

- Now lets use the foil method to multiply the two brackets

∵ (x + 4)(x - 2) = x² - 2x + 4x - 8 ⇒ collect the like terms

∴ (x + 4)(x - 2) = x² + 2x - 8

∴ y = x² + 2x - 8

* Now lets find the value of a and b to find the x-coordinate

 of the vertex point

∵ a = 1 , b = 2

∵ x-coordinate of the vertex = -b/2a

∴ x = -2/2(1) = -1

- Substitute the value of x in y

∴ y = (-1)² + 2(-1) - 8 = 1 - 2 - 8 = -9

∴ The vertex point is (-1 , -9)

* The vertex point is (-1 , -9)

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

a - base

b - exponent

so,