Consider the quadratic function y = 0.3 (x-4)2 - 2.5 Determine the axis of symmetry, x =
1 answer:
Answer:
Step-by-step explanation:
We have the quadratic function:
And we want to determine its axis of symmetry.
Notice that this is in vertex form:
Where (<em>h, k</em>) is the vertex of the parabola.
From our function, we can see that <em>h</em> = 4 and <em>k</em> = -2.5. Hence, our vertex is the point (4, -2.5).
The axis of symmetry is equivalent to the <em>x-</em>coordinate of the vertex.
The <em>x-</em>coordinate of the vertex is 4.
Therefore, the axis of symmetry is <em>x</em> = 4.
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Answer:
(x - 8)² = 20(y + 6)
Step-by-step explanation:
The focus of the parabola is (8,-1) and the equation of the directrix is y = - 11.
So, the parabola opens up and the axis of symmetry is x = 8 line.
Now, the axis of symmetry and the directrix meet at the point (8,-11).
So, the vertex of the parabola will be the midpoint of (8,-1) and (8,-11) i.e. (8,-6).
Now, half of the distance between the focus and the directrix is = a = units.
So, the equation of the parabola in vertex form will be
(x - 8)² = 4 × 5 × (y + 6)
⇒ (x - 8)² = 20(y + 6) (Answer)