How do you write a quadratic function in intercept form whose graph has x intercepts -4,1 and passes through (-3,-4)?

Question

Eva Abramson · Accepted Answer

#f(x) = x^2+3-4#. For how, please see below.

Given that the #x# intercepts are #-4# and #1#, we know that the functions factors as #f(x) = a(x+4)(x-1)# Now we can use the fact that #f(-3) = -4# to find #a# #-4 = a((-3)+4)((-3)-1)# #-4 = a(1)(-4)# so #a = 1# #f(x) = (x+4)(x-1)# #f(x) = x^2+3-4#

Jameson Allen · Answer

undefined To write a quadratic function in intercept form given x-intercepts and a point, follow these steps:

1. Use the x-intercepts to form the factors of the quadratic equation.
2. Multiply the factors to form the quadratic equation.
3. Use the given point to determine the value of the constant term in the equation.

Given x-intercepts -4 and 1, the factors of the quadratic equation are (x + 4) and (x - 1).
Multiplying the factors, we get: $ f(x) = a(x + 4)(x - 1) $.

Now, use the given point (-3, -4) to find the value of 'a'.
Substitute x = -3 and f(x) = -4 into the equation and solve for 'a'.

$$
-4 = a(-3 + 4)(-3 - 1) \
-4 = a(1)(-4) \
-4 = -4a \
a = 1
$$

Thus, the quadratic function in intercept form is:
$$ f(x) = (x + 4)(x - 1) $$