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ohaa [14]
3 years ago
15

Find the x-intercept of the parabola with vertex (1,-13) and y-intercept (0,-11).

Mathematics
2 answers:
nikitadnepr [17]3 years ago
6 0
Standard form of equation for a parabola: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of vertex
using given coordinates of vertex:
y=A(x-1)^2-13
using given coordinates of y-intercept:
-11=A(0-1)^2-13
A=2
Equation of parabola: y=2(x-1)^2-13
x-intercepts

set y=0
0=2(x-1)^2-13
2(x-1)^2=13
(x-1)^2=13/2
x-1=±√(13/2)
x=1±√(13
Advocard [28]3 years ago
4 0
1. find equation

general solutions are:
y = a x^{2} +bx +c \\ \\ \frac{dy}{dx} = 2ax +b

for P(0,-11)

-11 = 0a + 0b +c ⇒c = -11

for p(1,-13)
-13 = 1a + 1b -11 \\ a+b = -2

and

0 = 2a + b \\ b = -2a

solve for a and b:
a - 2a = -2 \\ a = 2 \\ b = -4

the total equation is now:

y = 2 x^{2} -4x -11

To find the x-intercept set y=0 and solve for x

0 = 2 x^{2} -4x-11
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