+0  
 
+3
184
1
avatar+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 

Best Answer 

 #1
avatar+81051 
+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.....

GRAPH

CPhill  Jan 28, 2015
Sort: 

1+0 Answers

 #1
avatar+81051 
+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.....

GRAPH

CPhill  Jan 28, 2015

19 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details