Mathematics, 12.11.2020 07:20 imlexi12393

Please help! what is an equation of a parabola with x-intercepts at (2,0) and (-7,0) and which passes through the point (1,32)?

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Answer from: erinrae

f(x)=-4(x-2)(x+7)

Or, in standard form:

f(x)=-4x^2-20x+56

Step-by-step explanation:

We can use the factored form of a quadratic equation:

f(x)=a(x-p)(x-q)

Where a is the leading coefficient and p and q are the zeros of the quadratic.

We know that the x-intercepts are at (2, 0) and (-7, 0).

So, let's substitute 2 for p and -7 for q. This yields:

f(x)=a(x-2)(x+7)

Now, we need to determine a.

We know that it passes through the point (1, 32). In other words, if we substitute 1 for x, we should get 32 for f(x). Therefore:

32=a(1-2)(1+7)

We can now solve for a. First, compute:

32=a(-1)(8)

Multiply:

32=-8a

Divide both sides by -8:

a=-4

So, the value of a is -4.

Therefore, our entire equation is:

f(x)=-4(x-2)(x+7)

Notes:

We can expand this into standard form:

$f(x)=-4(x-2)(x+7) \\ f(x)=-4(x^2+5x-14) \\ f(x)=-4x^2-20x+56$

Answer from: Quest

x=6 and x=3

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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.

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Please help! what is an equation of a parabola with x-intercepts at (2,0) and (-7,0) and which passe...