ACT Preparation / Unit 10 ACT 0923 worked example, 60 to 90 seconds
Matching a Graph to Its Equation
The idea
To match a graph with an equation, work in three steps. First, identify the base shape: a line, a parabola, a V, a square-root curve. Second, read the key point, such as the vertex or the starting point, and compare it with the base function's: the horizontal and vertical moves give h and k. Third, check the direction and steepness: opening down means a negative a, and a narrower shape means a larger size of a. Confirm with one more point.
In practice
Worked example: a V-shaped graph opens downward with its vertex at (2, 3) and passes through (3, 1). Base shape: |x|. Vertex (2, 3): y = a|x − 2| + 3. Opening down: a is negative. At (3, 1): 1 = a|1| + 3, so a = −2. The equation is y = −2|x − 2| + 3.
Where people slip
Check the sign inside the bars against the vertex: a vertex at x = 2 means x − 2, not x + 2.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Unlocks
- Nothing yet depends on this.
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