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# Parabola

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The red parabola shown is the graph of the equation ay^2 + by + c = x. Find a + b + c.

Jun 15, 2022

#1
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Plug in the point $$(0,0)$$ into the equation.

This gives us: $$0a + 0b + c = 0$$, meaning $$c = 0$$

Now, plug in the point $$(1,2)$$ into the equation. This gives us: $$1 =4a + 2b$$

Lastly, plug in the point $$(1,-2)$$ into the equation. This gives us $$1 = 4a - 2b$$

Solving this system, we find $$b = 0$$ and $$a = {1 \over 4 }$$.

Thus, $$a + b + c = \color{brown}\boxed{1 \over 4}$$

Jun 15, 2022

#1
+2448
0

Plug in the point $$(0,0)$$ into the equation.

This gives us: $$0a + 0b + c = 0$$, meaning $$c = 0$$

Now, plug in the point $$(1,2)$$ into the equation. This gives us: $$1 =4a + 2b$$

Lastly, plug in the point $$(1,-2)$$ into the equation. This gives us $$1 = 4a - 2b$$

Solving this system, we find $$b = 0$$ and $$a = {1 \over 4 }$$.

Thus, $$a + b + c = \color{brown}\boxed{1 \over 4}$$

BuilderBoi Jun 15, 2022