新SAT数学OG样题-Multiple choice题型例题（3）

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The graph of y = (2x - 4)(x - 4) is a parabola in the xy-plane. In which

of the following equivalent equations do the x- and y-coordinates of the vertex of the parabola appear as constants or coefficients?

新SAT数学OG样题-Multiple choice题型解析汇总，点击查看

Content: Passport to Advanced Math

Key: C

Objective: You must be able to see structure in expressions and equations

and create a new form of an expression that reveals a specific property.

Explanation: Choice C is correct. The equation y = (2x - 4)(x - 4) can be

written

in vertex form, y = a + k, to display the vertex, (h, k), of the parabola. To

put

the equation in vertex form, first multiply: (2x - 4)(x -4) = 2

-8x-4x+16.

Then, add like terms, - 8x - 4x +16 = - 12x + 16. The next step is com-

pleting the square.

Therefore, the coordinates of the vertex, (3, -2), are only both revealed

in

choice C. Since you are told that all of the equations are equivalent,

simply

knowing the form that displays the coordinates of the vertex will save all

of

these steps — this is known as "seeing structure in the expression or

equation."