Question

PLS HELP 2. Write a quadratic function to the model to the graph to the right

Answer 1

Given the vertex, (-4, 3):

We can use the quadratic function in vertex form, f(x) = a(x - h)^2 + k where:

(h, k) = vertex

a = determines whether the graph opens up or down, and makes the parent function wider or narrower.
* If a is positive, the graph opens up.
* If a is negative, the graph opens down.

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

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

Now that we defined each variable in the vertex form, we can plug in the values of the vertex (-4, 3) into the equation:

f(x) = a(x - h)^2 + k
f(x) = a(x + 4)^2 + 3

To solve for the value of “a”, we must choose another point from the graph. The y-intercept of the parabola happens to be (0, 19), so we’ll use its values to solve for “a”:

19 = a(0 + 4)^2 + 3
19 = a(4)^2 + 3
19 = a(16) + 3

Subtract 3 from both sides:

19 - 3 = a(16) + 3- 3

16 = 16a

Divide both sides by 16:

16/16 = 16a/16

1 = a

The value of a = 1. Since it is a positive number, then it confirms that the parabola opens upward.

Therefore, the quadratic function in vertex form is:

f(x) = (x + 4)^2 + 3

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