X^2+ 6x + 8 Vertex: Axis of symmetry: Y-intercept: X-intercept:
2 answers:
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).
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Alright, lets get started.
Justin is asked to solve the linear equations using elimination method.
By using elimination method means we have to multiply some numbers in our given equations in such a way that the co-efficient of x or y become same in both equations so that we could add or subtract them to cancel one of the term either x or y.
So, given equations are :
See we have 5x in first equation and -20x in second equation.
So, we try to change 5x into 20 x by multiplying it with 4, both of the equations will have 20 x in common
Lets multiply 4 in first equation
Now both equations could be added and 20 x will be cancelled out and we could easily find the value of y then solve for x.
So, Justin should try to change 5 so that it will be cancels, so option B : Answer
Hope it will help :)