determine the coordinates of the x-intercepts and the y-intercept of the parabola
$y = x^2 + 6x + 5$

(if applicable, give your answer as a decimal.)

x-intercepts: $( \quad , \quad )$ and $( \quad , \quad )$

y-intercept: $( \quad , \quad )$

Question

determine the coordinates of the x-intercepts and the y-intercept of the parabola
$y = x^2 + 6x + 5$

(if applicable, give your answer as a decimal.)

x-intercepts: $( \quad , \quad )$ and $( \quad , \quad )$

y-intercept: $( \quad , \quad )$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Solving for Variables" ], "new_concepts": [ "Parabola Intercepts", "Quadratic Factoring" ], "current_concepts": [ "Solving for Variables", "Parabola Intercepts", "Quadratic Factoring" ] } ## Find the x-intercepts $$ \begin{aligned} &y = 0 \ &x^2 + 6x + 5 = 0 \ &(x + 5)(x + 1) = 0 \ &x = -5 \quad \text{or} \quad x = -1 \ &\text{Coordinates: } (-5, 0) \text{ and } (-1, 0) \end{aligned} $$ ## Find the y-intercept $$ \begin{aligned} &x = 0 \ &y = 0^2 + 6(0) + 5 \ &y = 5 \ &\text{Coordinates: } (0, 5) \end{aligned} $$ Determine the coordinates of the x-intercepts and the y-intercept of the parabola $y = x^2 + 6x + 5$ (If applicable, give your answer as a decimal.) x-intercepts: (-5, 0) and (-1, 0) y-intercept: (0, 5) { "elements": [ { "type": "functiongraph", "params": [ { "js": "x*x + 6*x + 5", "latex": "x^2 + 6x + 5" }, -7, 1 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "name": "y = x^2 + 6x + 5", "withLabel": true } }, { "type": "point", "params": [ [-5, 0] ], "properties": { "name": "(-5,0)", "size": 4, "strokeColor": "#F2557F", "fillColor": "#F2557F", "withLabel": true } }, { "type": "point", "params": [ [-1, 0] ], "properties": { "name": "(-1,0)", "size": 4, "strokeColor": "#F2557F", "fillColor": "#F2557F", "withLabel": true } }, { "type": "point", "params": [ [0, 5] ], "properties": { "name": "(0,5)", "size": 4, "strokeColor": "#5583F2", "fillColor": "#5583F2", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Parabola Intercepts" ] }

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QUESTION IMAGE

Question

Explanation:

Find the x-intercepts

Find the y-intercept

Answer: