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Start by factoring out y.
How can you eliminate the constant?
How can you eliminate the constant?
How can you eliminate the constant?
After each equation has been simplified, what are they all missing?
y_1=0 and y_2=6
n_1=0 and n_2=- 5
t_1=0 and t_2=7
x_1=0 and x_2=- 9
They are all quadratic equations without a constant term.
When we have a quadratic equation written in the form x^2+bx=0, we can solve this by factoring out the variable and then solving the resulting equation with the Zero Product Property.
Factor out y
Use the Zero Product Property
(II): LHS+6=RHS+6
Notice that both sides of the equation contain a 7. Therefore, if we subtract 7 from both sides, we end up with an equivalent equation but without a constant. This can be solved by the Zero Product Property like we did in Part A.
LHS-7=RHS-7
Factor out n
Use the Zero Product Property
(II): LHS-5=RHS-5
Like in Part B, we can solve this with the Zero Product Property if we first eliminate the constant from both sides.
LHS-3=RHS-3
Factor out 2t
.LHS /2.=.RHS /2.
Use the Zero Product Property
(II): LHS+7=RHS+7
Like in Parts B and C, we can solve this equation with the Zero Product Property if we first eliminate the constant from both sides.
LHS+4=RHS+4
LHS * 3=RHS* 3
Factor out x
Use the Zero Product Property
(II): LHS-9=RHS-9
Graphically, the solutions to a quadratic expression set equal to zero are its x-intercepts. Since all of the quadratic equations are without a constant, this means they intercept the y-axis at the origin, which also constitutes one of the x-intercepts.