+152 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
+128474 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.....
+128474 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.....
