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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All triangles will add up to 180 degrees so subtract 58 from that and divide that by 2
|4x+3|=9+2x if we square both sides, we can eliminate the absolute values signs...
16x^2+24x+9=81+36x+4x^2 subtract the right side from both sides
12x^2-12x-72=0 now we can factor
12(x^2-x-6)=0
12(x^2+2x-3x-6)=0
12(x(x+2)-3(x+2)=0
12(x-3)(x+2)
So:
x= -2 or 3
Hence, the correct answer is: C) (x - 6)^2 = 45
Further explanation:
Given equation is:
We will move the constant term on other side of the equation
To complete the square, we will take the coefficient of x and divide it by 2, as we already know that one term is x.
So, adding (6)^2 on both sides
Hence, the correct answer is: C) (x - 6)^2 = 45
Keywords: Quadratic Equation, Solution of equation
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It is graph b, its negative
