Answer:
m = 11
Step-by-step explanation:
Since the points are collinear then the slope between points are equal.
Calculate the slope m using the slope formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (1, - 1)
m = =
=
Repeat with
(x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (m, 4)
m = =
=
Cross- multiply
m - 1 = 10 ( add 1 to both sides )
m = 11
Find the vertex:
Determine if the parabola will open up or down:
Since the value of a is positive, the parabola will open upwards
Find the x and y intercepts:
Factor to find the x intercepts
(x+8)(x+2)
x + 8 = 0
x = -8
x + 2 = 0
x = -2
x intercepts:
x = -2
x = -8
Find the y intercept
Hence, C. Graph A best represents the quadratic function