Water is coming out of a fountain is modeled by the function f(x)=-x^2+8x+2 where f(x) represents the height, in feet, if the wa
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For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
Where:
m: It's the slope
b: It is the cut-off point with the y axis.
According to the statement data we have:
Thus, the equation is of the form:
We substitute the given point and find the cut-off point:
Finally, the equation is:
We manipulate algebraically to obtain the standard form:
We multiply by 3 on both sides of the equation:
We multiply by -1 on both sides:
Answer:
Considering the definition of vertex, the vertex form of y = –3x² – 12x – 2 is y=a(x+2)²+10 , where (-2,10) is the vertex of the parabola.
<h3>Vertex form</h3>The function f(x) = ax² + bx + c
with a, b, c real numbers and a ≠ 0, is a function quadratic expressed in its polynomial form (It is so called because the function is expressed by a polynomial).
The quadratic function can be expressed by the vertex form of a quadratic equation: y=a(x−h)²+k , where (h,k)= vertex of the parabola.
The formula to find the value x of the vertex of a quadratic equation is
To calculate the value of y of the vertex, it is necessary to find the numerical value of "x vertex" in the polynomial expression. This is:
(h,k)= (,
)
In this case:
- a= -3
- b= -12
- c= -2
Replacing in the formula to find the value x of the vertex of a quadratic equation, you get:
Solving:
<u><em>x= -2</em></u>
The value of y of the vertex can be calculated as:
y = –3×(-2)² – 12×(-2) – 2
Solving:
y= –3×4 – 12×(-2) – 2
y= –12 +24 – 2
<u><em>y=10</em></u>
Finally, the vertex form of y = –3x² – 12x – 2 is y=a(x+2)²+10 , where (-2,10) is the vertex of the parabola.
Learn more about vertex form of a cuadratic function:
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