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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Aubra because you always round to the greater value if the number is 5-9
You only round down if the number at the end is 0-4
Answer:
∠A = 99°
Step-by-step explanation:
Complementary angles sum to 180°, thus
∠A + ∠B = 180 ← substitute values
2x - 23 + x + 20 = 180
3x - 3 = 180 ( add 3 to both sides )
3x = 183 ( divide both sides by 3 )
x = 61
Hence
∠A = 2x - 23 = (2 × 61) - 23 = 122 - 23 = 99°
