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If the vertex of the parabola y = ax^2 + bx + c is at (1, -2), what is the value
If the vertex of the parabola y = ax^2 + bx + c is at (1, -2), what is the value of a if b = 4 and c = -6?
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If the vertex of the parabola y = ax^2 + bx + c is at (1, -2), what is the value of a if b = 4 and c = -6?
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The vertex form of a parabola is given by x = -b/(2a). Here, 1 = -4/(2a) => 2a = -4 => a = -2.
Questions & Step-by-step Solutions
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Q: If the vertex of the parabola y = ax^2 + bx + c is at (1, -2), what is the value of a if b = 4 and c = -6?
Solution:
The vertex form of a parabola is given by x = -b/(2a). Here, 1 = -4/(2a) => 2a = -4 => a = -2.
Steps: 7
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Step 1: Identify the formula for the x-coordinate of the vertex of a parabola, which is x = -b/(2a).
Step 2: Substitute the given value of b (which is 4) into the formula: x = -4/(2a).
Step 3: Set the x-coordinate of the vertex (which is 1) equal to the expression from Step 2: 1 = -4/(2a).
Step 4: To eliminate the fraction, multiply both sides of the equation by 2a: 2a * 1 = -4.
Step 5: This simplifies to 2a = -4.
Step 6: Now, solve for a by dividing both sides by 2: a = -4 / 2.
Step 7: Calculate the value: a = -2.
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