**Unformatted text preview: **tercepts, we set P (x) = 0 and solve −1.5x2 + 170x − 150 = 0. The mere
thought of trying to factor the left hand side of this equation could do serious psychological
damage, so we resort to the quadratic formula, Equation 2.5. Identifying a = −1.5, b = 170,
and c = −150, we obtain 2.3 Quadratic Functions 145 x=
=
=
= √ b2 − 4ac
2a
−170 ± 1702 − 4(−1.5)(−150)
2(−1.5)
√
−170 ± 28000
−3
√
170 ± 20 70
3
−b ± √ √ We get two x-intercepts: 170−20 70 , 0 and 170+20 70 , 0 . To ﬁnd the y -intercept, we set
3
3
x = 0 and ﬁnd y = P (0) = −150 for a y -intercept of (0, −150). To ﬁnd the vertex, we use
the fact that P (x) = −1.5x2 + 170x − 150 is in the general form of a quadratic function and
170
appeal to Equation 2.4. Substituting a = −1.5 and b = 170, we get x = − 2(−1.5) = 170 .
3
170
14000
To ﬁnd the y -coordinate of the vertex, we compute P 3 = 3 and ﬁnd our vertex is
170 14000
. The axis of symmetry is the vertical line passing through the vertex so it i...

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