What is the answer to this

Mathematics

1 answer:

Softa [21]3 years ago

7 0

Answer:

5 f

Re-order terms so that constants are on the left

. 5

5 f

solution

5 f

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I’ll use “x” as “a number”

So it’s basically asking if-

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Vertex (0,1) x intercepts is - 1 and 1 what is the equation of the parabola?

MrRa [10]

$\bf y=a(x-{{ h}})^2+{{ k}}\\
x=a(y-{{ k}})^2+{{ h}}\qquad\qquad vertex\ ({{ h}},{{ k}})$

those are the vertex form of a parabola... so hmmm
the vertex of this one is at 0,1 and intercepts or "solutions" are at -1 and 1, so is opening downwards, notice the picture below

that means, the squared variable is the "x", thus the form is $\bf y=a(x-{{ h}})^2+{{ k}}$

now, we know the vertex is at 0,1, and two x-intercepts of $\pm 1,0$

thus $\bf y=a(x-{{ h}})^2+{{ k}}\qquad 
\begin{cases}
h=0\\
k=1\\
when
\\
x=\pm 1\\
y=0
\end{cases}
\\\\\\
\textit{so.. hmmm let us use the point ... say hmmm 1,0}
\\\\
y=a(x-{{ h}})^2+{{ k}}\implies 0=a(1-0)^2+1$

solve for "a", to see what that coefficient is, then plug it back in the vertex form equation