Plzzzzz help! will mark Brainliest!!!
2 answers:
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Step-by-step explanation:
A quadratic function is a second-degree polynomial function with the general form
,
where ,
, and
are real numbers, and
.
The standard form or the vertex form of a quadratic function is, however, a little different from the general form. To get the standard form from the general form, we need to use the "complete the square" method.
Let
and
,
then the expression reduces into
,
where the point (<em>h</em>, <em>k</em>) are the coordinates for the vertex of the quadratic function.
There are two different methods to approach this question. First, we consider the general form of the quadratic function, it is observed that has a y-intercept at the point , so
.
Additionally, it is pointed that two distinct points and
lies on the quadratic graph, hence
and
.
Subtract equation (1) from equation (2) term-by-term,
Substitute into equation (1),
.
Therefore, the equation of the quadratic function is
.
Alternatively, the vertex of the quadratic function is given as the point , substitute these coordinates into the vertex form of a quadratic function.
.
Substitute the point into the function above,
.
Therefore, the general form of the quadratic function is
.