Question

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Explanation:

To address this, we analyze quadratic function forms:

Key Concepts:

• Vertex Form of a quadratic function is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. The vertex \((h, k)\) directly gives the maximum (if \(a < 0\)) or minimum (if \(a > 0\)) value of the function.
• Standard Form is \( y = ax^2 + bx + c \), which requires using the formula \( x = -\frac{b}{2a} \) (and then substituting back) to find the vertex/maximum/minimum.

Filling the Blanks:

1. The first blank (after "using the"): vertex (since vertex form is more efficient for finding max/min).
2. The second blank (after "value of"): vertex (the maximum/minimum occurs at the vertex of the parabola).
3. The third blank (after "value of"): k (in vertex form \( y = a(x - h)^2 + k \), \( k \) is the maximum/minimum value).
4. The fourth blank (after "from its"): vertex (the vertex form directly reveals the vertex \((h, k)\), so \( k \) is the max/min).

for Efficiency:
If a data set includes the maximum or minimum value (the vertex), using vertex form is more efficient. Vertex form \( y = a(x - h)^2 + k \) immediately shows the vertex \((h, k)\), where \( k \) is the maximum (if \( a < 0 \)) or minimum (if \( a > 0 \)) value. Standard form requires additional calculations (e.g., \( x = -\frac{b}{2a} \)) to find the vertex, making vertex form faster here.

Final Answers (Filling the Blanks):

1. using the \(\boldsymbol{\text{vertex}}\) form...
2. value of the \(\boldsymbol{\text{vertex}}\)...
3. value of \(\boldsymbol{k}\)...
4. from its \(\boldsymbol{\text{vertex}}\) form...

(For the original question: "Is it more efficient to use vertex form or standard form...?" The answer is vertex form, as it directly provides the maximum/minimum value via the vertex \((h, k)\) without extra calculations needed for standard form.)

Answer:

for Efficiency:
If a data set includes the maximum or minimum value (the vertex), using vertex form is more efficient. Vertex form \( y = a(x - h)^2 + k \) immediately shows the vertex \((h, k)\), where \( k \) is the maximum (if \( a < 0 \)) or minimum (if \( a > 0 \)) value. Standard form requires additional calculations (e.g., \( x = -\frac{b}{2a} \)) to find the vertex, making vertex form faster here.

Final Answers (Filling the Blanks):

1. using the \(\boldsymbol{\text{vertex}}\) form...
2. value of the \(\boldsymbol{\text{vertex}}\)...
3. value of \(\boldsymbol{k}\)...
4. from its \(\boldsymbol{\text{vertex}}\) form...

(For the original question: "Is it more efficient to use vertex form or standard form...?" The answer is vertex form, as it directly provides the maximum/minimum value via the vertex \((h, k)\) without extra calculations needed for standard form.)