Find the x-intercept(s) and the coordinates of the vertex for the parabola.
1 answer:
Answer:
see explanation
Step-by-step explanation:
Given
y = x² - 2x - 8
To find the x- intercepts let y = 0 , that is
x² - 2x - 8 = 0 ← in standard form
(x - 4)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 2 = 0 ⇒ x = - 2
x- intercepts : x = - 2, x = 4
The x- coordinate of the vertex is mid way between the x- intercepts, that is
=
=
= 1
Substitute x = 1 into the equation for corresponding y- coordinate
y = 1² - 2(1) - 8 = 1 - 2 - 8 = - 9
vertex = (1, - 9 )
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Answer:
The measure of anle MNP is
- m ∠ MNP = (x - y)/2
Explanation:
The image attached shows the figure corresponding to this question.
The <em>angle MNP</em>, wich is also the angle LNP, is formed by the intersection of a secant and a tanget to a circle.
Then, you can use the theorem:
- the angle formed by a secant and a tangent to a circle that intersect outside the circle is half the difference of the major arc minus the minor arc.
The major arc formed is identified with the letter x and the minor arc is identified witht he letter y. Thus, the measure of the angle MNP is half the differenc x - y:
- m ∠ MNP = (x - y)/2
