The vertex of this parabola is at (2,-1) when the y value is 0 and then x value is 5 what is the coefficient of the squared term
in the parabolas equation
2 answers:
Answer:
Step-by-step explanation:
Remark
The general formula for the vertex of a parabola is
y = a(x - b) + c
What you know from the vertex is the formula describes b and c and the y intercept gives you the information to solve for a.
Solution
y = a(x - 2)^2 - 1 If you graph this, the vertex should be at (2,-1). I'll upload the graph at the end.
Now we need to solve for a
x = 0
y = 5
5 = a(0 - 2)^2 - 1
5 = a(4) - 1 Add 1 to both sides.
6 = a(4) Divide by 4
6/4 = a 4/4 Switch
a = 3/2
Answer
y = 3/2 (x - 2)^2 - 1
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Answer:
AB = 13.89
Measure of angle A = 59.74°
Measure of angle B = 30.26°
Step-by-step explanation:
The given parameters are;
∠C = 90°
AC = 7
BC = 12
Part 1
Hence, the question has the dimensions of the two adjacent sides of the right angle (angle 90°)
From Pythagoras theorem, we have;
A² = B² + C²
Where, A is the opposite side to the right angle, hence;
In the ΔABC,
AB ≡ A
Therefore;
AB² = AC² + BC² = 7² + 12² = 193
∴ AB = √193 = 13.89
Part 2
∠A is the side opposite side BC such that by trigonometric ratios
∴ ∠A = Arctan(1.714) or tan⁻¹(1.714) = 59.74°
Part 3
∠B is found from knowing that the sum of the angles in a triangle = 180°
∴ ∠A + ∠B + ∠C = 180° which gives
59.74° + 90° + ∠B = 180°
Hence, ∠B = 180° - (59.74° + 90°) = 180° - 149.74° = 30.26°.