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