What is the value of A and B and if you can please show how you got that answer

Mathematics

1 answer:

son4ous [18]3 years ago

3 0

Answer:

a = 4.5 units

b = 7.5 units

Step-by-step explanation:

By using mean proportional theorem in the ΔACB,

ΔACB ~ ΔADC ~ ΔCDB

$\frac{AD}{CD}=\frac{CD}{DB}$

$\frac{8}{6}=\frac{6}{a}$

a = $\frac{6\times 6}{8}$

a = 4.5

$\frac{AB}{CB}=\frac{CB}{DB}$

$\frac{(a+8)}{b}=\frac{b}{a}$

Since a = 4.5

$\frac{4.5+8}{b}=\frac{b}{4.5}$

b² = 4.5 × 12.5

b = √56.25

b = 7.5 units

Therefore, a = 4.5 units and b = 7.5 units will be the answer.

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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