Question

Match each quadratic function to its graph.
f(x)=x2+2
g(x)=2x2–16x+30=2(x–3)(x–5)
h(x)=
–
x2+2x–1=
–
(x–1)2
k(x)=2x2+16x+32=2(x+4)2

Answer 1

I don't see the graphs here, so below are the key identifying features for each quadratic — use these to match them to the graphs.

f(x) = x^2 + 2
- Vertex: (0, 2) (minimum)
- Opens upward (a = 1)
- y-intercept: 2
- No real x-intercepts (never crosses x-axis)

g(x) = 2x^2 − 16x + 30 = 2(x − 3)(x − 5)
- Vertex: (4, −2) (minimum)
- Opens upward and is narrower than f (a = 2)
- x-intercepts: x = 3 and x = 5
- y-intercept: 30

h(x) = −x^2 + 2x − 1 = −(x − 1)^2
- Vertex: (1, 0) (maximum)
- Opens downward (a = −1)
- Touches the x-axis at x = 1 (double root, tangent)
- y-intercept: −1

k(x) = 2x^2 + 16x + 32 = 2(x + 4)^2
- Vertex: (−4, 0) (minimum)
- Opens upward and is narrower (a = 2)
- Touches the x-axis at x = −4 (double root, tangent)
- y-intercept: 32

Match each graph by finding its vertex, direction (up/down), whether it crosses or only touches the x-axis, and relative width (a = 1 vs a = 2).