Answer:
The zeros are the points where the parabola intercepts the x-axis.
![\sf x = 7 \implies x - 7 = 0](https://tex.z-dn.net/?f=%5Csf%20x%20%3D%207%20%5Cimplies%20x%20-%207%20%3D%200)
![\sf x = 1 \implies x - 1 = 0](https://tex.z-dn.net/?f=%5Csf%20x%20%3D%201%20%5Cimplies%20x%20-%201%20%3D%200)
where a is some constant
If the parabola passes through point (3, 4) then:
![\sf \implies a(3 - 7)(3 - 1) = 4](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20a%283%20-%207%29%283%20-%201%29%20%3D%204)
![\sf \implies a(-4)(2) = 4](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20a%28-4%29%282%29%20%3D%204)
![\sf \implies -8a = 4](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20-8a%20%3D%204)
![\sf \implies a = -\dfrac12](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20a%20%3D%20-%5Cdfrac12)
So the equation of the parabola is:
![\sf y = -\dfrac12(x - 7)(x - 1)](https://tex.z-dn.net/?f=%5Csf%20y%20%3D%20-%5Cdfrac12%28x%20-%207%29%28x%20-%201%29)
Or in standard form:
![\sf y = -\dfrac12x^2+4x-\dfrac72](https://tex.z-dn.net/?f=%5Csf%20y%20%3D%20-%5Cdfrac12x%5E2%2B4x-%5Cdfrac72)
Answer: 24=8x3
Step-by-step explanation:i think so i hope this helps
Answer:
2 minutes 56 seconds
Step-by-step explanation:
Answer:
(
, 8 )
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 10x - 2 ← is in slope- intercept form
with slope m = 10
Parallel lines have equal slopes
then the tangent to the parabola with a slope of 10 is required.
the slope of the tangent at any point on the parabola is ![\frac{dy}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D)
differentiate each term using the power rule
(a
) = na
, then
= 6x + 2
equating this to 10 gives
6x + 2 = 10 ( subtract 2 from both sides )
6x = 8 ( divide both sides by 6 )
x =
= ![\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D)
substitute this value into the equation of the parabola for corresponding y- coordinate.
y = 3(
)² + 2
= (3 ×
) + 2
=
+ ![\frac{8}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B3%7D)
= ![\frac{24}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B24%7D%7B3%7D)
= 8
the point on the parabola with tangent parallel to y = 10x - 2 is (
, 8 )