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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We have a quadratic function written in standard form. $y=ax_{2}+bx+c $ This kind of equation can give us a lot of information about the parabola by observing the values of $a,$ $b,$ and $c.$ $y=-6x_{2}+6x−1⇔y=-6x_{2}+6x+2 $ We see that for the given equation, $a=-6,$ $b=6,$ and $c=2.$

Consider the point at which the curve of the parabola changes direction.

This point is the vertex of the parabola, and defines the axis of symmetry. If we want to calculate the $x-$value of this point, we can substitute the given values of $a$ and $b$ into the expression $-2ab $ and simplify.$-2ab $

$-2(-6)6 $

Simplify

$0.5$

The point at which the graph of a parabola changes direction also defines the maximum or minimum point of the graph. Whether the parabola has a minimum or maximum is determined by the value of $a.$

Since the given value of $a$ is$y=-6x_{2}+6+2$

Substitute$x=0.5$

$y=-6⋅0.5_{2}+6⋅0.5+2$

CalcPowCalculate power

$y=-6⋅0.25+6⋅0.5+2$

MultiplyMultiply

$y=-1.5+3+2$

AddSubTermsAdd and subtract terms

$y=3.5$

Given the standard form of a parabola, the $(x,y)$ coordinates of its vertex can be expressed in terms of $a$ and $b.$ $(x,y)⇔(-2ab ,f(-2ab )) $ We've already calculated both of these values above, so we know that the vertex lies on the point $(0.5,3.5).$

The $y-$intercept of a quadratic function written in standard form is given by the value of $c.$ $y=-6x_{2}+6x+2 $ Therefore, the $y-$intercept is $2.$