Find the vertex, focus, directrix, and axis of symmetry ofeach parabola (without completing the square ), and determinewhether the parabola opens upward of downward. y = 2x^2 + 4x - 3

dredyue

dredyue

Answered question

2022-08-08

Find the vertex, focus, directrix, and axis of symmetry of each parabola (without completing the square ), and determine whether the parabola opens upward of downward.
y = 2 x 2 + 4 x 3

Answer & Explanation

Raelynn Johnson

Raelynn Johnson

Beginner2022-08-09Added 13 answers

First of all, the positive value of the x 2 term tells you that it opens upward;
To find the x coordinate of the vertex : x =- b / 2a = -4 / 2(2) = -1
Then plug inzero for x to get the y value of thevertex:
y = 2 x 2 + 4 x 3
= 2 ( 1 ) 2 + 4 ( 1 ) 3 = 2 4 3 = 5 So the vertex is ( -1, -5).
The axis of symmetry goes through the vertex, along the direction that the parabola opens - in this case, along the line x = -1.
Focus and directrix are found by : c =1 / 4a = 1 / (4 * 2) = 1/8.
So the focus is 1/8 of a unit up from the vertex, at ( -1, -4 7/8), and the directrix is 1/4 unit down from the vertex,at
y = -5 1/8

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