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Leni [432]
3 years ago
9

X^2+ 6x + 8 Vertex: Axis of symmetry: Y-intercept: X-intercept:

Mathematics
2 answers:
algol133 years ago
6 0

Answer:

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

Step-by-step 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).

Bogdan [553]3 years ago
4 0

Answer:

( + 2 ) ( + 4 )

Step-by-step explanation:

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