What is h(x)h(x)=-5x^2+10x+15 ?

The solution to h(x)h(x)=-5x^2+10x+15 is Ellipse with (h,k)=(1,0),a=2,b=2sqrt(5)

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h(x)h(x)=-5x^2+10x+15

h (x) h (x) = - 5 x^{2} + 10 x + 15

(h, k) = (1, 0), a = 2, b = 25

Solution steps

yy = - 5 x^{2} + 10 x + 15

Rewrite

yy + 5 x^{2} - 10 x - 15 = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{2 ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 0), a = 2, b = 25

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 0), b = 25, a = 2

9 x^{2} + y^{2} - 81 = 0

\frac{x ^{2}}{4} + \frac{( y - 4 ) ^{2}}{16} = 1

16 x^{2} + 80 y^{2} = 1280

\frac{5 x ^{2} + y ^{2} - 15 x + 8 y - 11}{4} = 0

\frac{x ^{2} + y ^{2} + 4 x - 8 y - 6}{x ^{2} + y ^{2} + 6 x + 2 y + 9} = \frac{4}{5}

What is h(x)h(x)=-5x^2+10x+15 ?
The solution to h(x)h(x)=-5x^2+10x+15 is Ellipse with (h,k)=(1,0),a=2,b=2sqrt(5)