Given y = 3x^2 + 24x + 43

a. Transform to vertex form

b. Write the coordinates of the vertex

c. Find the x-intercepts

d. Sketch the graph, showing the vertex, x- and y- intercepts, and symmetrical point

ihavelovedyousincewewere18
Jan 28, 2015

#1**+13 **

y = 3x^2 + 24x + 43 factor out the 3

y =3 (x^2 + 8x + 43/3) complete the square

y = 3( x^2 +8x + 16 + 43/3 - 16) factor the first three terms

y = 3[ (x + 4)^2 - 5/3 ] distribute the 3 back

y = 3(x + 4)^2 - 5

The coordinate of the vertex is (-4, -5)

The x intercepts are about (-5.291, 0) and (-2.709, 0)

The y intercept is at (0,43)

The line of symmetry is x = -4

Here's the graph.......notice that both equations are exactly the same graph.....

CPhill
Jan 28, 2015

#1**+13 **

Best Answer

y = 3x^2 + 24x + 43 factor out the 3

y =3 (x^2 + 8x + 43/3) complete the square

y = 3( x^2 +8x + 16 + 43/3 - 16) factor the first three terms

y = 3[ (x + 4)^2 - 5/3 ] distribute the 3 back

y = 3(x + 4)^2 - 5

The coordinate of the vertex is (-4, -5)

The x intercepts are about (-5.291, 0) and (-2.709, 0)

The y intercept is at (0,43)

The line of symmetry is x = -4

Here's the graph.......notice that both equations are exactly the same graph.....

CPhill
Jan 28, 2015