Question

Solve each of the quadratic equations below and describe what the solution(s) represent to the graph of each.
x2 – 36 = 0 and x2 = 8x – 12

Part 2: Using complete sentences, compare and contrast the graphs of y = x2 − 36 and y + x2 = 8x − 12.

Answer 1

x=+/- 6
and to second x2-8x+12=0
x_1,_2=(8+/- sqrt(64-48))/2 = (8+/- 4)/2 = 2 and 6

Answer 2

x^2-36=0 use difference of squares
so (x-6)(x+6)=0
then what values of x make the equation true? in this case x=6,-6
the graph crosses the x axis at these points, because for these xs y=0.
x^2=8x-12
x^2-8x+12=0
quadratic equation: x=(8+/-sqrt(8^2-4*1*12))/2
x=(8+/-sqrt(16))/2
x=4+/-2
x=2,6
so the graph crosses the x axis at 2 and 6

Answer 3

Quaddratic A:x=6,-6 B:x=6,2 Graph A: http://mathway.com/graph_image.aspx?p=y=x2-36?p=520?p=450?p=False?p=False?p=False?p=False?p=True?p=True?p=True?p=True?p=-40?p=40?p=-40?p=40?p=4 Graph B: http://mathway.com/graph_image.aspx?p=y+x2=8x-12?p=520?p=450?p=False?p=False?p=False?p=False?p=True?p=True?p=True?p=True?p=-20?p=20?p=-20?p=20?p=4

Answer 4

the graph opens up, the x^2 term is positive, so it has a minimum point.
vertex (x coordinate)=-b/2a
-4/2=-2
plug it back into the original equation
(-2,-16)
x intercepts= x=-6,2

Answer 5

Create your own unique quadratic equation in the form y = ax2 + bx + c that opens the same direction and shares one of the x-intercepts of the graph of y = x2 + 4x − 12.

Explain whether the graph has a maximum or minimum point.
Find the vertex and x-intercepts of the graph.

Answer 6

make sure a is positive, and pick numbers so that when y=0, x=-6 or 2 will make the equation true. the graph has a minimum point, because it opens upward, and use the formula -b/2a to find the x coordinate of the vertex

Answer 7

Example Please?