A car averages 60 miles per hour on a road trip. Use a graph to show the relationship between the time and distance traveled. Wh
1 answer:
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Answer:
Step-by-step explanation:
I'm not sure how you are finding this in class, but the easiest way by far is to use the expressions for h and k:
and
(Just a fun fact: Those expressions come from the quadratic formula that help us to factor a quadratic equation.)
Filling in for h:
simplifies to
Filling in for k:
which simplifies a bit to
which simplifies a bit more to
The vertex, then, is (4, -25).
You would also find this if you completed the square. But again, I'm not sure how you're solving for the vertex in class.
Answer:
Step-by-step explanation:
To find the intercept with the x axis, we make h (x) = 0.
0 = (x + 1) ^ 2 - 4
0 = x ^ 2 + 2x + 1 -4
0 = x ^ 2 + 2x - 3
0 = (x +3) (x-1)
x = 1
x = -3
To find the intercept with the y axis, we make x = 0.
y = (0+1)^2 -4
y = -3
For a quadratic equation of the form ax ^2 + bx+ c
The vertex is calculated with the formula x = -b/2a
So:
x = -2/2(1)
x = -1
Finally the axis of symmetry of a quadratic function always passes through the vertex.
So:
x = -1
Below is a graph for this function, where you can see the cut points with the axes, the vertex and axis of symmetry
