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We have been given graph of a downward opening parabola with vertex at point . We are asked to write equation of the parabola in standard form.
We know that equation of parabola in standard form is .
We will write our equation in vertex form and then convert it into standard form.
Vertex for of parabola is , where point (h,k) represents vertex of parabola and a represents leading coefficient.
Since our parabola is downward opening so leading coefficient will be negative.
Upon substituting coordinates of vertex and point (0,0) in vertex form, we will get:
Divide both sides by
So our equation in vertex form would be .
Let us convert it in standard from.
Therefore, the equation of function is standard form would be .
Given:
Two lines intersect each other.
Consider the below figure attached with this question.
To find:
The value of x.
Solution:
If two lines intersect each other then the vertically opposite angles are congruent and their measures are equal.
In the given figure, the measures of two vertically opposite angles are (2x+29)° and (9x-13)°.
Divide both sides by -7.
Therefore, the value of x is 6.
