Question

Please help.

Three quadratic functions are being compared to determine which has the smallest y-intercept. The first quadratic function can be modeled by the equation a(x) = (x + 5)2 − 7. The second function, b(x), can be modeled by the values presented in the table. The third quadratic function, c(x), is graphed below. Which quadratic function has the smallest y-intercept and what is this value?

x b(x)
−3 0
0 6
3 0

a(x) has the smallest y-intercept: −7.
b(x) has the smallest y-intercept: −3.
c(x) has the smallest y-intercept: −2.
a(x) has the smallest y-intercept: −5.

Answer 1

To find the smallest y-value, you substitute x=0 into each other the functions.

For function a(x), do a(0):
a(0) = (0+5)2-7 = 3

For function b(x), it gives you (0,6).

For function c(x), just look at where the line crosses the x-axis. It crosses it as -2, and there's a point at (0,-2).

So since -2 is the smallest, function c(x) has the smallest y-intercept: -2