Two of the factors of ax^2+bx+c are (2x-2) and (x+5). Which is one of the x-intercepts of y=ax^2+bx+c?
A. -2
B. -1
C. 5
D. 1
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If the factors are (2x-2)(x+5), then
(2x-2)(x+5) = ax^2 + bx + c
and 2x-2 = 0 ----> x = 1
or x+5 = 0 , -----> x = -5
which one is given?
Its D. 1?
To find the x-intercept of a quadratic function, you need to set y equal to zero and solve for x. In this case, the equation is y=ax^2+bx+c, and we are given that two factors of this quadratic equation are (2x-2) and (x+5).
Step 1: Set y equal to zero.
0 = ax^2 + bx + c
Step 2: Replace ax^2 + bx + c with its factored form.
0 = (2x-2)(x+5)
Step 3: Apply the zero product property, where if a product of factors equals zero, then at least one of the factors must equal zero.
(2x-2)(x+5) = 0
Step 4: Set each factor equal to zero and solve for x.
2x-2 = 0 or x+5 = 0
Solving the first equation:
2x = 2
x = 2/2
x = 1
Solving the second equation:
x = -5
Therefore, the possible x-intercepts are x = 1 and x = -5. From the given options, the correct answer is:
D. 1