Mathematics: Quadratic Relations?

The given equation that relates h (= height above the water) to x (= horizontal distance from starting point) is

h = -(x - 1)² + 11

h = -x² + 2x + 10

When she hits the water, h = 0, so

0 = -x² + 2x + 10

0 = x² - 2x - 10

Solve this quadratic equation using the discriminant:

√D = √( (-2)² - 4×1×(-10) ) = 6.633

x₁ = (2 + 6.633) / (2×1) = 4.32

x₂ = (2 - 6.633) / (2×1) = -2.32

A negative value makes no sense in this case, so the only valid solution is

x = 4.3 (in meters)

a polynomial of degree 2( this is, the utmost skill of the variable in that's 2) is talked approximately as a quadratic polynomial. as an occasion: x^2 + x + a million, 5x^2 + 3x., (a million/2)*x^2. if we draw the graph of a quadratic equation, we are able to verify that that's a verify talked approximately as a parabola. a quadratic equation has somewhat 2 roots ( 2 specific values of x make y akin to 0). Its graph cuts the x-axis at 2 aspects and those 2 aspects are the roots of the equation. whilst a=0, ax^2 will become 0. for this reason the polynomial will now no longer have degree 2. So, a should not be akin to 0 if the expression is to proceed to be a quadratic polynomial.