# The parabola shown is the graph of f(x) = Ax^{2} + 2x + C. The x-intercepts of the graph are at -4 and -3. Find the exact value of the y-intercept and the coordinates of the vertex of the graph (expressed in terms of rational numbers and radicals).

The parabola shown is the graph of
The x-intercepts of the graph are at Find the exact value of the y-intercept and the coordinates of the vertex of the graph (expressed in terms of rational numbers and radicals).
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jlo2niT
Given:

x intercept are
We need to write x intercept in factor form
If p and q are the factors then intercepts form of quadratic equation is

are x intercepts

Now compare f(x) with out given f(x)

$7a=2$
$a=\frac{2}{7}$
Replace the value in f(x), then f(x) becomes

To find out vertex we use formula
$x=\frac{-b}{2a}$

now we find out y

$x=\frac{-7}{2}$

Vertex

Now find out y intercept when $x=0$

y intercept is $\left(\frac{24}{7}\right)$