Find the equation for the parabola that passes through the point (-2,-4), with vertex at (3,1) and a vertical axis
1 answer:
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (3, 1), hence
y = a(x - 3)² + 1
To find a substitute (- 2, - 4) into the equation
- 4 = a(- 2 - 3)² + 1
- 4 = 25a + 1 ( subtract 1 from both sides )
25a = - 5 ( divide both sides by 25 )
a = - = -
y = - (x - 3)² + 1 ← in vertex form
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Answer:
The true statements are:
m∠ 3 + m∠ 4 = 180° ⇒ 1st
m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ 2nd
m∠ 2 + m∠ 4 = m∠ 5 ⇒ 3rd
Step-by-step explanation:
* Look to the attached diagram to answer the question
# m∠ 3 + m∠ 4 = 180°
∵ ∠ 3 and ∠ 4 formed a straight angle
∵ The measure of the straight angle is 180°
∴ m∠ 3 + m∠ 4 = 180° ⇒ <em>true</em>
# m∠ 2 + m∠ 4 + m∠ 6 = 180°
∵ ∠ 2 , ∠ 4 , ∠ 6 are the interior angles of the triangle
∵ The sum of the measures of interior angles of any Δ is 180°
∴ m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ <em>true</em>
# m∠ 2 + m∠ 4 = m∠ 5
∵ In any Δ, the measure of the exterior angle at one vertex of the
triangle equals the sum of the measures of the opposite interior
angles of this vertex
∵ ∠ 5 is the exterior angle of the vertex of ∠ 6
∵ ∠2 and ∠ 4 are the opposite interior angles to ∠ 6
∴ m∠ 2 + m∠ 4 = m∠ 5 ⇒ <em>true </em>
# m∠1 + m∠2 = 90°
∵ ∠ 1 and ∠ 2 formed a straight angle
∵ The measure of the straight angle is 180°
∴ m∠1 + m∠2 = 90° ⇒ <em>Not true</em>
# m∠4 + m∠6 = m∠2
∵ ∠ 4 , ∠ 6 , ∠ 2 are the interior angles of a triangle
∵ There is no given about their measures
∴ We can not says that the sum of the measures of ∠ 4 and ∠ 6 is
equal to the measure of ∠ 2
∴ m∠4 + m∠6 = m∠2 ⇒ <em>Not true</em>
<em></em>
# m∠2 + m∠6 = m∠5
∵ ∠ 5 is the exterior angle at the vertex of ∠ 6
∴ m∠ 2 + m∠ 6 = m∠ 5 ⇒ <em>Not true</em>
