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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Answer:
D
Step-by-step explanation:
The standard form for a parabola is ax^2+bx+c. In this equation, b=0 and c=0. For g(x), you would plug in your y-value that was given (which is 4) and you would plug in your x-value that that given (which is 1). Use PEMDAS. The correct answer is the one that is true.
A. g(x) = (4x)^2
4 = (4(1))^2
4 = 16. (not true)
B. g(x) = 1/4 x^2
4 = 1/4 (1)^2
4 = 1/4 (not true)
C. g(x) = 16x^2
4 = 16(1)^2
4 = 16 (not true)
D. g(x) = 4x^2
4 = 4(1)^2
4 = 4. (true --> correct answer)
The answer is b 60 degrees <span />