Mathematics, 21.06.2019 17:40 beck1013

Find the x-intercepts of the parabola withvertex (1,1) and y-intercept (0,-3).write your answer in this form: (x1,if necessary, round to the nearest hundredth.

Answers: 1

Show answers

Answers

Answer from: 1341220857

$(\frac{1}{2},0),(\frac{3}{2},0)$

Step-by-step explanation:

The vertex form of a parabola is given by:

y=a(x-h)^2+k , where V(h,k) is the vertex of the parabola.

The given parabola has vertex (1,1).

This implies that: h=1,k=1 .

Put these values into the vertex form equation.

$\implies y=a(x-1)^2+1$

The y-intercept of this parabola is: (0,-3).

This point lies on the parabola hence it must satisfy its equation.

$\implies -3=a(0-1)^2+1$

$\implies -3=a(-1)^2+1$

$\implies -3=a(1)+1$

$\implies -3=a+1$

$\implies -3-1=a$

$\implies -4=a$

The equation now becomes

$\implies y=-4(x-1)^2+1$

To find the x-intercept, put y=0 into the equation:

$\implies -4(x-1)^2+1=0$

$\implies -4(x-1)^2=-1$

Divide through by -4.

$\implies \frac{-4(x-1)^2}{-4}=\frac{-1}{-4}$

$\implies (x-1)^2=\frac{-1}{-4}$

$\implies (x-1)^2=\frac{1}{4}$

Take plus or minus square root of both sides.

$\implies x-1=\pm \sqrt{\frac{1}{4}}$

$\implies x-1=\pm \frac{1}{2}$

$\implies x=1\pm \frac{1}{2}$

$\implies x=1-\frac{1}{2}$ or $\implies x=1+ \frac{1}{2}$

$\implies x=\frac{1}{2}$ or $\implies x=1 \frac{1}{2}$

Therefore the x-intercepts are:

$(\frac{1}{2},0),(\frac{3}{2},0)$

To the nearest hundredth, we have 0.50,0),(1.50,0)

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

answerim :

step-by-step explanation:

im not sure but my dad knows

Another question on Mathematics

Mathematics, 21.06.2019 13:00

Liesl grew 7/12 of a foot in one year. her little sister grew 1/3 of a foot during that same year. how much more did liesl grow than her little sister did

Answers: 2

Answer

Mathematics, 21.06.2019 14:30

Its due ! write an equation in which the quadratic expression 2x^2-2x 12 equals 0. show the expression in factored form and explain what your solutions mean for the equation. show your work.

Answers: 1

Answer

Mathematics, 22.06.2019 00:00

Corresponding angles are a. always b. sometimes c. never congruent

Answers: 1

Answer

Mathematics, 22.06.2019 01:00

Asmall book publisher knows that 26 books weigh 41 lbs. how much do 40 books weigh?

Answers: 1

Answer

You know the right answer?

Find the x-intercepts of the parabola withvertex (1,1) and y-intercept (0,-3).write your answer in t...