What are the coordinates of the vertex of the function f(x)=x2 10x−3?
2 answers:
The coordinates of the vertex of the function is
(-5, -28).
It is given that the function
It is required to find the coordinates of the vertex.
<h3>What is a parabola?</h3>It is defined as the graph of a quadratic function that has something bowl-shaped.
We have a function:
This function represents a parabola.
We know the standard form of parabola in quadratic style:
By comparing the given function to the standard form of parabola, we get
a = 1, b = 10, and c = -3
The vertex of the parabola is given by:
Putting the values in the above equation, we get:
x = -5 put this value in the given parabola function, we get:
or y = -28
The coordintes = (x, y) : (-5 , -28) which is shown in the graph.
Thus, the coordinates of the vertex of the function is (-5, -28).
Know more about the parabola here:
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Answer: The correct option are as follows;
(1) The triangles are similar because corresponding sides are congruent
(2) The triangles are similar because alternate interior angles are congruent
(3) In the similar triangles, Angle 3 and Angle 6 are corresponding angles
Step-by-step explanation: Please refer to the picture attached for details.
The line i and line e has been drawn and marked as parallel lines. Also two transversal lines m and n have been drawn to intersect in the region between the parallel lines to form two triangles (as shown in the picture).
From the information given, where line e intersects with line n we have angle 1, and where line e intersects with line m we have angle 3, and then the third angle is angle 2.
Furthermore, where line l intersects line m we have angle 6, and where line l intersects line n is angle 4. Also in this second triangle, the third angle is 5.
Upon close observation we would see that Angle 6 is equal to Angle 3, since the transversal m has cut across both parallel lines l and e. Similarly Angle 4 is equal to Angle 1 since the transversal n has cut across parallel lines l and e. Having that Angles 3 and 1 are congruent to Angles 6 and 4, we can conclude that the value of the third angle in one triangle is equal to the that of the third in the second triangle, that is, Angle 2 equals Angle 5. Also, if the angles are similar and the lines l and e are parallel, then the lines formed in both triangles are equal.
So our conclusions are;
The interior angle are alternate angles (Angles 3 and 6, Angles 1 and 4), and the third interior angles are Opposite (Angles 2 and 5 {Opposite angles are equal})
