SOLVING QUADRATIC
EQUATIONS
14. Determine the number of real roots, the axis of symmetry, and the vertex of each equation.
a. y = x2 - 2x + 1
b. y = 4x2 + 2x + 8
6.3 =-222+42+6
15. Xander determines the roots for the quadratic equation x2 + 4x - 1 = 7. His work is shown.
x2 + 4x -1 = 7
a = 1, b = 4, c = -1
x＝
-4土V42-4（1）（-1）
2(1)
ェ
-4土v16+4
-4土V20
N
x12
-4土4.47
N
0.47 ~ 0.235 or
-8.47
~-4.235
The roots are approximately 0.235 and -4.235.
a. What did Xander do incorrectly?
b. Determine the roots for the given quadratic equation...
16. State if the product will be rational or irrational. Explain your reasoning.
a. V3V144
b. V81/V16
14.
a. Number of real roots: 1 real root
Axis of symmetry: x = 1
Vertex: (1, 0)
b. Number of real roots: 0 real roots
Axis of symmetry: x = -0.25
Vertex: (-0.25, 7.75)
6.3 = -2(2)2 + 4(2) + 6
= -8 + 8 + 6
= 6
The equation is not balanced correctly. The correct solution is x = 2.
15.
a. Xander incorrectly calculated the discriminant. The correct calculation should be:
(-4)^2 - 4(1)(-1) = 16 + 4 = 20
Therefore, the roots are not approximately 0.235 and -4.235.
b. x^2 + 4x - 1 = 7
x^2 + 4x - 8 = 0
Using the quadratic formula, the roots are approximately 1.83 and -5.83.
16.
a. The product V3V144 will be rational because V144 = 12, so the product is 3*12 = 36.
b. The product V81/V16 will be irrational because V81 = 9 and V16 = 4, so the final result will involve a square root and cannot be expressed as a fraction.