Find the x-intercept of a porabola with a vertex of (-3,-14) and y-intercept (0,-13)

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (- 3, - 14), thus

y = a(x + 3)² - 14

To find a substitute (0, - 13) into the equation

- 13 = 9a - 14 ( add 14 to both sides )

9a = 1 ( divide both sides by 9 )

a = , hence

y = (x + 3)² - 14 ← equation of parabola

To find the x- intercepts let y = 0

(x + 3)² - 14 = 0

Multiply through by 9

(x + 3)² - 126 = 0 ( add 126 to both sides )

(x + 3)² = 126 ( take the square root of both sides )

x + 3 = ± = ± 3

Subtract 3 from both sides

x = - 3 ± 3

The x- intercepts are therefore

x = - 3 - 3 ≈ - 14.22 ( to 2 dec. places ) or

x = - 3 + 3 ≈ 8.22 ( to 2 dec. places )

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.