Question

What is the equation written in vertex from of a parabola with a vertex of (4, –2) that passes through (2, –14)?

Answer 1

Answer:

y = -3(x - 4)² - 2

Step-by-step explanation:

Given the vertex, (4, -2), and the point (2, -14):

We can use the vertex form of the quadratic equation:

y = a(x - h)² + k

Where:

(h, k) = vertex

a  =  determines whether the graph opens up or down, and it also makes the parent function wider or narrower.

• positive value of a = opens upward
• negative value of a = opens downward
• a is between 0 and 1, (0 < a < 1) the graph is wider than the parent function.
• a > 1, the graph is narrower than the parent function.

h = determines how far left or right the parent function is translated.

• h = positive, the function is translated h units to the right.
• h = negative, the function is translated |h| units to the left.

k determines how far up or down the parent function is translated.

• k = positive: translate k units up.
• k = negative, translate k units down.

Now that I've set up the definitions for each variable of the vertex form, we can determine the quadratic equation using the given vertex and the point:

vertex (h, k): (4, -2)

point (x, y): (2, -14)

Substitute these values into the vertex form to solve for a:

y = a(x - h)² + k

-14 = a(2 - 4)²  -2

-14 = a (-2)² -2

-14 = a4 + -2

Add to to both sides:

-14 + 2 = a4 + -2 + 2

-12 = 4a

Divide both sides by 4 to solve for a:

-12/4 = 4a/4

-3 = a

Therefore, the quadratic equation inI vertex form is:

y = -3(x - 4)² - 2

The parabola is downward-facing, and is vertically compressed by a factor of -3. The graph is also horizontally translated 4 units to the right, and vertically translated 2 units down.

Attached is a screenshot of the graph where it shows the vertex and the given point, using the vertex form that I came up with.

Please mark my answers as the Brainliest, if you find this helpful :)