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If the parabola y = ax^2 + bx + c has its vertex at (1, -2), what is the value o
If the parabola y = ax^2 + bx + c has its vertex at (1, -2), what is the value of a if it passes through the point (0, 0)?
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Practice Questions
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Q1
If the parabola y = ax^2 + bx + c has its vertex at (1, -2), what is the value of a if it passes through the point (0, 0)?
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Using the vertex form y = a(x - 1)^2 - 2 and substituting (0, 0), we get 0 = a(0 - 1)^2 - 2 => 2 = a => a = 2.
Questions & Step-by-step Solutions
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Q: If the parabola y = ax^2 + bx + c has its vertex at (1, -2), what is the value of a if it passes through the point (0, 0)?
Solution:
Using the vertex form y = a(x - 1)^2 - 2 and substituting (0, 0), we get 0 = a(0 - 1)^2 - 2 => 2 = a => a = 2.
Steps: 5
Show Steps
Step 1: Understand that the vertex of the parabola is given as (1, -2). This means the parabola can be written in vertex form: y = a(x - 1)^2 - 2.
Step 2: We know the parabola passes through the point (0, 0). This means when x = 0, y should equal 0.
Step 3: Substitute x = 0 and y = 0 into the vertex form equation: 0 = a(0 - 1)^2 - 2.
Step 4: Simplify the equation: 0 = a(1) - 2, which simplifies to 0 = a - 2.
Step 5: Solve for a by adding 2 to both sides: a = 2.
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