Question

Consider the quadratic function: f(x)=2x^2−8x+2 . Find the following for this parabola.

A) The line of symmetry:

B) The vertex:

C) The vertical intercept is the point

D) Give the coordinates of the two xx intercepts of the parabola as ordered pairs.

Answer 1

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Griven that, fra) = 2x2= 84+2 ie. Pra) = 2(x2-4x) +2 ie. Pews = 264?- 4x + 4) +2-8 ie. fea) = 2(x-2)*+60) feas= a (x-2)²+k a(arn) ² tk, we get, companing with a i 2 ; ha a . and ka-6 so axis is ach ie 222 of symmetry (2,K) ventia . is (2,-6)

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free # Now implics, 2 (x-2)2–6 20 >> 6x-2)2-3=0 >> (2-2)=3 => x=2= I do 3 => 215 21.03 50, x-intoncepts ane (2-13,0) and (3,703,0) N #now y intercept is that point where a=0 = 2x0²_8X0 +2=2. y wintercept (0,2) so; os

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So the answers are,

(A) Line of symmetry : x = 2​​​​​​

(B) Vertex : (2, -6)​​​​​​

(C) Vertical Intercept :(0, 2)​​​​​​

(D) x-intercepts : (2 - √3, 0), (2 + √3, 0)