190k views
0 votes
X^2+ 6x + 8
Vertex:
Axis of symmetry:
Y-intercept:
X-intercept:

2 Answers

5 votes

Answer:

( + 2 ) ( + 4 )

Explanation:

User Jayesh Bhoyar
by
8.5k points
7 votes

Answer:

See below for answers and explanations (along with a graph)

Explanation:

To calculate the vertex, we can transform the expression into an equation in the form of y=a(x-h)²+k and take (h,k) as our vertex. By completing the square, we see that y=x²+6x+8 is the same as y=(x+3)²-1, implying that our vertex is (-3,-1)

To calculate the axis of symmetry, it is defined as the vertical line that passes the x-axis, defined as x=h, therefore the axis of symmetry is x=-3

To calculate the y-intercept, it is defined as the y-value when x=0, therefore the y-intercept would be y=(0)^2+6(0)+8=8, so y=8 or (0,8)

To calculate the x-intercepts, which are the x-values when y=0, we can factor the expression and set it equal to 0 so we can use the Zero Product Property. Therefore, if x²+6x+8=0, then (x+2)(x+4)=0, implying that x+2=0 and x+4=0 are solutions. This means that our x-intercepts are x=-2 and x=-4 or (-2,0) and (-4,0).

Note that there are different ways to achieve these answers. See the graph for a visual reference (you may need to click on it to zoom in).

X^2+ 6x + 8 Vertex: Axis of symmetry: Y-intercept: X-intercept:-example-1
User Aptriangle
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories