Quick Check Solutions Graphing Quadratics Target D
1) \(f(x) = -3(x – 7)(x – 1)\)
Form: Intercept/Factored
Key Feature: \(x\)-intercepts \((7, 0)\) and \((1, 0)\)
2) \(g(x) = (x + 6)^2 – 2\)
Form: Vertex
Key Feature: vertex \((-6, 2)\)
3) In order to find the vertex of \(k(x) = (x + 4)(x + 2)\), you need to convert the function into vertex form. Since you cannot directly convert from intercept form to vertex form, you need to convert into standard form first by using the distributive property: \(k(x) = x^2 + 6x + 8\). Then you can convert this function into vertex form by completing the square: \
(k(x) = (x + 3)^2 - 1\). So the key feature of the graph of the function, the vertex, would be at \((-3, -1)\).
4) In order to find the \(x-\)intercepts of \(h(x) = 2x^2 – 10x – 12\), you need to convert the function into intercept/factored form: \(h(x) = 2(x - 6)(x + 1)\). So the key feature of the graph of the function, the x-intercepts, would be at \((6, 0)\) and \((-1, 0)\).
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1) \(f(x) = -3(x – 7)(x – 1)\)
Form: Intercept/Factored
Key Feature: \(x\)-intercepts \((7, 0)\) and \((1, 0)\)
2) \(g(x) = (x + 6)^2 – 2\)
Form: Vertex
Key Feature: vertex \((-6, 2)\)
3) In order to find the vertex of \(k(x) = (x + 4)(x + 2)\), you need to convert the function into vertex form. Since you cannot directly convert from intercept form to vertex form, you need to convert into standard form first by using the distributive property: \(k(x) = x^2 + 6x + 8\). Then you can convert this function into vertex form by completing the square: \
(k(x) = (x + 3)^2 - 1\). So the key feature of the graph of the function, the vertex, would be at \((-3, -1)\).
4) In order to find the \(x-\)intercepts of \(h(x) = 2x^2 – 10x – 12\), you need to convert the function into intercept/factored form: \(h(x) = 2(x - 6)(x + 1)\). So the key feature of the graph of the function, the x-intercepts, would be at \((6, 0)\) and \((-1, 0)\).
Back to Guided Learning