Given the vertex, (-4, 3):
We can use the quadratic function in vertex form, f(x) = a(x - h)^2 + k where:
(h, k) = vertex
a = determines whether the graph opens up or down, and makes the parent function wider or narrower.
* If a is positive, the graph opens up.
* If a is negative, the graph opens down.
h = determines how far left or right the parent function is translated.
k = determines how far up or down the parent function is translated.
Now that we defined each variable in the vertex form, we can plug in the values of the vertex (-4, 3) into the equation:
f(x) = a(x - h)^2 + k
f(x) = a(x + 4)^2 + 3
To solve for the value of “a”, we must choose another point from the graph. The y-intercept of the parabola happens to be (0, 19), so we’ll use its values to solve for “a”:
19 = a(0 + 4)^2 + 3
19 = a(4)^2 + 3
19 = a(16) + 3
Subtract 3 from both sides:
19 - 3 = a(16) + 3- 3
16 = 16a
Divide both sides by 16:
16/16 = 16a/16
1 = a
The value of a = 1. Since it is a positive number, then it confirms that the parabola opens upward.
Therefore, the quadratic function in vertex form is:
f(x) = (x + 4)^2 + 3
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Question
The table shows the heights in a basketball team.
Height: 198, 199, 200, 201, 202
a.) Work out the mean height of the team. Round you answer to 1d.p.
That, I have worked out is 200.3
b.) A new player joins the team and raises the mean average height to 201cm. Work out the height of the new player.
Answer:
206 cm
Step-by-step explanation:
The sum of the fiven numbers, 198+199+200+201+202=1000
For a mean of 201, the product should be 201*6=1206
The difference of the two is equivalent to the height of the other person hence 1206-1000=206 cm
Therefore, the height is 206 cm
Terri can swim 3 laps in 2.5 minutes. To find how long it takes to swim 20 laps, you can make a proportion.
Put the amount of laps on the top and the time(minutes) at the bottom.
Cross multiply:
Divide by 3:
It would take Terri 
OR 
minutes to run 20 laps.
Answer:
f(x) = −6(x + 1)(x + 5)
Step-by-step explanation:
f(x) = −6(x + 1)(x + 5) & f(x) = −5(x + 1)(x + 5) are the only ones on the correct side of the y-axis, and f(x) = −6(x + 1)(x + 5) has a y-intercept of -30.
