Question

1. y = x² + 5x + 6
A. The domain is:
B. The range is:
C. The x-intercept(s) islare:
D. The y-intercept is:
E. The vertex is:
F. The axis of symmetry is:
What’s the Answer to this

Answer 1

Domain is all real numbers
Range is y<5
X-5
Y-6
Vertex- 1
Axis of s- 1

Answer 2

A. The domain for a quadratic equation is ALL REAL NUMBERS OR (-~,~) negative infinity to positive infinity.

B).The possible values or Minimum value the graph can attain.

x=-b/2a(Note...This also corresponds to the vertex).

a=1

b=5

c=6

x= -b/2a = -5/2(1) = -5/2

To get the corresponding value for y... substitute x=-5/2 into the eqn

y=(-5/2)²+5(-5/2)+6

y=25/4 - 25/2 + 6

y=-1/4

Range (-5/2,-1/4)

C)To get x-intercept.

Values of x that satisfies the equation or the points where the graph crosses to the other side.

Set y=0

x²+5x+6=0

x²+3x+2x+6=0

By Grouping

(x²+3x)+(2x+6)=0

x(x+3)+2(x+3)=0

x+2=0 or x+3 =0

x=-2 or -3.

These are x-intercepts

D). To get y-intercept... Set x =0

Doing that

y=0²+5(0)+6

y=6.

This is the y-intercept.

E). The Vertex corresponds to the range

So the vertex is where the graph divides symmetrically or equally

(-5/2,-1/4).

F. Axis of symmetry = -b/2a = -5/2.