Question Write an equation for the quadratic graphed below: x-intercepts: (-1,0) and (4,0); y-intercept: (0,1)

Answer: y = (1/4)x² – (5/4)x + 1 Step-by-step explanation: The x-intercepts of the quadratic equation are simply it’s roots. Thus, we have; (x + 1) = 0 and (x – 4) = 0 Now, formula for quadratic equation is; y = ax² + bx + c Where c is the y intercept. At y-intercept: (0,1), we have; At (-1,0), thus; 0 = a(1²) + b(1) + 1 a + b = -1 – – – (1) At (4,0), thus; 0 = a(4²) + b(4) + 1 16a + 4b = -1 Divide both sides by 4 to get; 4a + b = -1/4 – – – (2) From eq 1, b = -1 – a Thus; 4a + (-1 – a) = -1/4 4a – 1 – a = -1/4 3a – 1 = -1/4 3a = 1 – 1/4 3a = 3/4 a = 1/4 b = -1 – 1/4 b = -5/4 Thus; y = (1/4)x² – (5/4)x + 1 Log in to Reply

Answer:

y = (1/4)x² – (5/4)x + 1

Step-by-step explanation:

The x-intercepts of the quadratic equation are simply it’s roots.

Thus, we have;

(x + 1) = 0 and (x – 4) = 0

Now, formula for quadratic equation is;

y = ax² + bx + c

Where c is the y intercept.

At y-intercept: (0,1), we have;

At (-1,0), thus;

0 = a(1²) + b(1) + 1

a + b = -1 – – – (1)

At (4,0), thus;

0 = a(4²) + b(4) + 1

16a + 4b = -1

Divide both sides by 4 to get;

4a + b = -1/4 – – – (2)

From eq 1, b = -1 – a

Thus;

4a + (-1 – a) = -1/4

4a – 1 – a = -1/4

3a – 1 = -1/4

3a = 1 – 1/4

3a = 3/4

a = 1/4

b = -1 – 1/4

b = -5/4

Thus;

y = (1/4)x² – (5/4)x + 1