Maths-
SAT
Easy
Question
In the xy-plane, the graph of y = 3x2 − 14x intersects the graph of y = x at the points (0, 0) and (a, a). What is the value of a ?
The correct answer is: 5
y = 3x2 – 14x ---------------1
Also y = x ---------------2
Equation 2 = equation 1
x = 3x2 – 14x
3x2 – 14x – x = 0
3x2 - 15x = 0
Solve using quadratic formula method
Completing the square method, factorization or calculator
By factorization,
The above, quadratic equation becomes
3x(x – 5) = 0
3x = 0 and x – 5 = 0
x = 0 and x = 5
Since y = x, the two intersecting points are (0,0) and (5,5)
Therefore, a = 5
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