Parabola help with x intercepts

Question

write an equation of a parabola with x-intercepts at (1/5, 0) and (-3, 0) which passes through the point (0, 3).

Answer 1

Hi Cammy V

y = -5x² - 14x + 3

Since your are given the x-intercepts and the y intercept you can use this information to find a

Using the factored from of the quadratic equation

y = a(x - p)(x - q) where p and q are the x intercpts

p = 1/5 =0.2

q = -3

y = a(x - 0.2)(x + 3)

Use the given coordinates for the y - intercept (0, 3) to solve for a

x = 0

y = 3

3 = a(0 - 0.2)(0 + 3)

3 = -0.6a

3/(-0.6) =-5 = a

y = -5(x - 0.2)(x + 3). this is the factored format

y = -5(x² + 3x - 0.2x - 0.6)

y = -5(x² + 2.8 - 0.6)

y = -5x² - 14x + 3 this is the general or standard format

I hope this helps you can graph both the factored format and the standard form by hand, on a graphing calculator, or a desmos.com to confirm and see all the given points. You can also put this into vertex format if you want and plot all three.

I hope this helps

Answer 2

through (0,3) with x intercepts 1/5 and -3

parabola is y = a(5x-1)(x+3) plug in (0,3) to solve for "a"

3 = a(-1)(3) = -3a

a = -1

y = -(5x-1)(x+3 = -(5x^2+14x -3)

y = -5x^2 -14x +3

Answer 3

Write an equation of a parabola with x-intercepts at (1/5, 0) and (-3, 0) which passes through the point (0, 3).

So we first start with an equation of a general parabola, I will give it to you in the factored form rather than standard or vertex form. Just know there are a few forms of the equation, factor form is what we want to use here with x-intercepts as given information.

y = a(x - r₁)(x - r₂)

r₁ is the first x-intercept, r₂ is the second x-intercept, a is a constant that controls the vertical stretch/compression.

We already have two of those given to us.

Plugging our x-intercepts in leaves us with

y = a(x - 1/5)(x - (-3))

At this point we can plug in our point (0,3) and solve for our constant a.

3 = a (0 - 1/5)(0 - (-3))

3 = a (-1/5)(3)

3 = a (-3/5)

-5 = a

Now we have all the information for our final equation

Factored Form: y = -5(x - 1/5)(x + 3)

We can convert this to either

Standard form: y= −5x² − 14x + 3

or Vertex Form: y= −5(x+57​)² + 64/4

Answer 4

y = a(x - 1/5)(x + 3); 3 = a(-3/5); a = -5; y = -5(x - 1/5)(x + 3); y = - 5x² - 14x + 3