Answer:
y = 4/3 (x + 3/4)(x - 1)
Step-by-step explanation:
Notice in the given pints that (1,0) is an x-intercept. Use the quadratic function form in x-intercept form and substitute the one x-intercept.
y = a(x-s)(x-s)
y = a(x-1)(x-s)
Substitute the two other points as x and y.
10 = a(3-1)(3-s) Substituted point (3,10)
-2 = a(0-1)(0-s) Substituted point (0, -2)
Simplify or rearrange the equations and see what can be substituted.
10 = a(3-1)(3-s)
10 = 2a(3-s)
10 = 6a - as
-2 = a(0-1)(0-s)
-2 = (-a)(-s)
-2 = as Notice "as" is also in the other formula.
Substitute -2 for as
10 = 6a - as
10 = 6a - (-2)
10 = 6a + 2
8 = 6a
a = 8/6
a = 4/3
Include a=4/3 in the quadratic function in x-intercept form.
y = a(x-1)(x-s)
y = (4/3)(x-1)(x-s) Substitute random point (3,10) and find "s"
10 = (4/3)(3-1)(3-s)
10 = (4/3)(2)(3-s)
10 = (4/3)(6 - 2s)
10 = 8 - (8/3)s
2 = -(8/3)s
s = 2 ÷ -8/3
s = -0.75 = -3/4
You can write the equation in x-intercept form.
y = 4/3 (x + 3/4)(x - 1)
You can expand to write in standard form.
