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Quadratic or Not?
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Quadratic or Not?
Help Camila sort snow-day equations by function type. A quadratic function can be written as y = ax² + bx + c, where a ≠ 0. In this form, the sign of a tells whether its parabola opens up or down. Show your reasoning when asked.
Spot the Quadratic
Decide whether each rule is quadratic. Look for a nonzero x² term and check whether any other operations change the function type.
1.Which rule is a quadratic function?
- y = 4x² − 3x + 1
- y = 4x − 3
- y = x³ + 1
- y = 6/x
2.Mateo says y = (x − 5)(x + 2) is not quadratic because it is written as a product instead of ax² + bx + c. Is Mateo correct? Explain briefly.
3.For y = −2x² + 7x − 1, does the parabola open upward or downward? Name the coefficient that determines this.
4.Classify each rule as quadratic or not quadratic. If it is quadratic, state whether its graph opens up or down: (a) y = 0.5x² − 4; (b) y = −3x + 8; (c) y = −x² + 6x.
5.True or false: y = 9 is a quadratic function because it can be written as y = 0x² + 9. Explain using the value of a.
6.Complete the rule: In y = ax² + bx + c, a quadratic function must have a x² term, and the value of a must be .
7.Match each equation to its graph description.
- A. y = x²
- B. y = −x² + 4
- C. y = 2x + 1
- D. y = x³
- 2. Parabola opening upward
- 1. Straight line
- 3. Parabola opening downward
- 4. S-shaped cubic curve
8.Ravi is checking y = 3x² + 12x + 12. Factor the expression, then state the x-value where the graph touches the x-axis.
9.A snowball's height is modeled by h = −16t² + 24t + 2, where t is time in seconds and h is height in feet. Is this model quadratic? Does its graph open up or down? Give a reason.
10.Write one quadratic rule that opens upward and one that opens downward. For each rule, identify the value of a.
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