Mathematics, 02.04.2021 07:50 sallonquarts

For the function : f(x) = -(x-2)^2+9 name all transformations, intercepts and the vertex

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Answer from: rakanmadi87

Given:

The given function is:

f(x)=-(x-2)^2+9

To find:

The transformations, intercepts and the vertex.

Solution:

The vertex form of a parabola is:

y=a(x-h)^2+k ...(i)

Where, a is a constant and (h,k) is vertex.

If a<0, then the graph of parent quadratic function y=x^2 reflect across the x-axis.

If h<0, then the graph of parent function shifts h units left and if h>0, then the graph of parent function shifts h units right.

If k<0, then the graph of parent function shifts k units down and if k>0, then the graph of parent function shifts k units up.

We have,

f(x)=-(x-2)^2+9 ...(ii)

On comparing (i) and (ii), we get

a=-1,h=2,k=9

So, the graph of the parent function reflected across the x-axis, and shifts 2 units right and 9 units up.

Putting x=0 in (ii), we get

f(0)=-(0-2)^2+9

f(0)=-4+9

f(0)=5

The y-intercept is 5.

Putting f(x)=0 in (ii), we get

0=-(x-2)^2+9

(x-2)^2=9

Taking square root on both sides, we get

$(x-2)=\pm \sqrt{9}$

$x=\pm 3+2$

$x=3+2\text{ and }x=-3+2$

$x=5\text{ and }x=-1$

Therefore, the x-intercepts are -1 and 5.

The values of h and k are 2 and 9 respectively and (h,k) is the vertex of the parabola.

Therefore, the vertex of the parabola is (2,9).

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

Answer from: Quest

The answer is b: step 2.

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