Write a formula for quadratic function if its graph has the vertex at point ( 1/3 ,−3) and passes through the point (1,1).
1 answer:
Answer:
f(x) = 9(x -1/3)^2 -3
Step-by-step explanation:
In vertex form the equation of a quadratic with vertical scale factor "a" and vertex (h, k) is ...
y = a(x -h)^2 +k
To make the equation have (1, 1) as a solution, we need to find the value of "a". We can put the point coordinates in the equation and solve for "a":
1 = a(1 -1/3)^2 -3 . . . . . for (h, k) = (1/3, -3) as given
1 = (4/9)a -3 . . . . simplify
4 = (4/9)a . . . . . . add 3
9 = a . . . . . . . . . . multiply by 9/4
The quadratic function you desire is ...
f(x) = 9(x -1/3)^2 -3
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Hey there!
In order to turn a fraction into a decimal, simply divide the numerator by the denominator. The numerator is the top part of the fraction while the denominator is the bottom part of the fraction.
So,
as a decimal would be 0.9. Simply divide 9 by 10
Answer: 0.9
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In order to turn a fraction into a decimal, simply divide the numerator by the denominator. The numerator is the top part of the fraction while the denominator is the bottom part of the fraction.
So,
Answer: 0.9
Thank you for being part of the Brainly community!
Answer:
4 m
Step-by-step explanation:
The equation can be written ...
y = (x/4)² = (1/16)x²
where the divisor 4 is the horizontal scale factor that makes the parabola 8 m wide at y = 1 m.
This can also be written as ...
y = 1/(4p)x² = (1/16)x²
from which we can see ...
4p = 16
p = 4
In this form, p is the distance from the vertex to the focus, 4 meters.
_____
Another way to find the y-coordinate of the focus is to draw a line with slope 1/2 through the vertex. It will intersect the parabola at the point where the vertical distance to the directrix is the same as the horizontal distance to the focus. The y-coordinate of that point is the y-coordinate of the focus.
